Numerical Simulation, An Art of Prediction, Volume 2: Examples [2] 978-1-119-69475-5

Table of contents :
TABLE OF CONTENTS
Foreword ix

Introduction xi

Chapter 1. Agriculture 1

1.1. Feeding the world 2

1.2. Agriculture is being digitized 7

1.3. Decision-making support 10

1.4. Environmental impact 16

1.5. Plant growth 23

Chapter 2. Air and Maritime Transport 31

2.1. The long march of globalization 32

2.2. Going digital! 35

2.3. Optimum design and production 50

2.3.1. Lightening the structures 50

2.3.2. Mastering processes 53

2.3.3. Producing in the digital age 58

2.4. Improving performance 63

2.4.1. Increasing seaworthiness 63

2.4.2. Limiting noise pollution 68

2.4.3. Protecting from corrosion 76

2.4.4. Reducing energy consumption 78

Chapter 3. The Universe and the Earth 87

3.1. Astrophysics 88

3.1.1. Telling the story of the Universe 90

3.1.2. Observing the formation of celestial bodies 105

3.1.3. Predicting the mass of stars 109

3.2. Geophysics 114

3.2.1. Earthquakes 115

3.2.2. Tsunamis 120

3.2.3. Eruptions 127

Chapter 4. The Atmosphere and the Oceans 133

4.1. Meteorological phenomena, climate change 134

4.2. Atmosphere and meteorology 137

4.2.1. Global and local model 138

4.2.2. Scale descent 142

4.3. Oceans and climate 145

4.3.1. Marine currents 145

4.3.2. Climate 155

Chapter 5. Energies 165

5.1. The technical dream 165

5.2. Combustion 168

5.3. Nuclear energy 173

5.3.1. Dual-use energy 173

5.3.2. At the heart of nuclear fission 176

5.3.3. Developing nuclear fusion 183

5.4. New energies 188

5.4.1. Hydroelectricity 189

5.4.2. Wind energy 193

Chapter 6. The Human Body 199

6.1. A digital medicine 200

6.2. Medical data 206

6.2.1. Medical imaging 206

6.2.2. Genetic information 211

6.3. Mechanical behavior of muscles and organs 215

6.4. Blood circulation 216

6.4.1. Blood microcapsules 218

6.4.2. Angioplasty simulation 219

6.5. Cosmetics 227

6.6. Neurosciences 228

Chapter 7. Individuals and Society 237

7.1. Calculated choices 238

7.2. A question of style 241

7.2.1. Assigning a work to its author 243

7.2.2. Understanding a pictorial technique 245

7.2.3. Discovering a personality type 247

7.3. The shape of a city 253

7.3.1. Transport 254

7.3.2. Sound atmosphere 256

7.3.3. Businesses 260

7.4. A question of choice 263

7.5. What about humans? 272

Conclusion 281

Glossary of Terms 287

References 317

Index 353

Citation preview

Numerical Simulation, An Art of Prediction 2

To Marie, Julie, Louise and Claire, To Emil and Léonard, children of the 21st Century

Series Editor Gilles Pijaudier-Cabot

Numerical Simulation, An Art of Prediction 2 Examples

Jean-François Sigrist

First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd 2020 The rights of Jean-François Sigrist to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019950844 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-432-2

Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1. Agriculture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.1. Feeding the world . . . . . . . 1.2. Agriculture is being digitized 1.3. Decision-making support . . . 1.4. Environmental impact . . . . 1.5. Plant growth . . . . . . . . . .

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Chapter 2. Air and Maritime Transport. . . . . . . . . . . . . . . . . . . . .

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2.1. The long march of globalization . 2.2. Going digital!. . . . . . . . . . . . . 2.3. Optimum design and production . 2.3.1. Lightening the structures . . . 2.3.2. Mastering processes . . . . . . 2.3.3. Producing in the digital age . . 2.4. Improving performance . . . . . . . 2.4.1. Increasing seaworthiness . . . 2.4.2. Limiting noise pollution . . . . 2.4.3. Protecting from corrosion . . . 2.4.4. Reducing energy consumption

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Chapter 3. The Universe and the Earth . . . . . . . . . . . . . . . . . . . . . . . .

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3.1. Astrophysics . . . . . . . . . . . . . . . . . . . . . 3.1.1. Telling the story of the Universe . . . . . . . 3.1.2. Observing the formation of celestial bodies 3.1.3. Predicting the mass of stars . . . . . . . . . .

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3.2. Geophysics . . . 3.2.1. Earthquakes 3.2.2. Tsunamis . . 3.2.3. Eruptions . .

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Chapter 4. The Atmosphere and the Oceans . . . . . . . . . . . . . . . .

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4.1. Meteorological phenomena, climate change 4.2. Atmosphere and meteorology . . . . . . . . . 4.2.1. Global and local model . . . . . . . . . . 4.2.2. Scale descent . . . . . . . . . . . . . . . . 4.3. Oceans and climate . . . . . . . . . . . . . . . 4.3.1. Marine currents . . . . . . . . . . . . . . . 4.3.2. Climate . . . . . . . . . . . . . . . . . . . .

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Chapter 6. The Human Body. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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165 168 173 173 176 183 188 189 193

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6.1. A digital medicine . . . . . . . . . . . . . . . . 6.2. Medical data . . . . . . . . . . . . . . . . . . . 6.2.1. Medical imaging . . . . . . . . . . . . . . 6.2.2. Genetic information . . . . . . . . . . . . 6.3. Mechanical behavior of muscles and organs 6.4. Blood circulation . . . . . . . . . . . . . . . . 6.4.1. Blood microcapsules . . . . . . . . . . . . 6.4.2. Angioplasty simulation . . . . . . . . . . 6.5. Cosmetics . . . . . . . . . . . . . . . . . . . . . 6.6. Neurosciences . . . . . . . . . . . . . . . . . .

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Chapter 5. Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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134 137 138 142 145 145 155

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5.1. The technical dream . . . . . . . . . 5.2. Combustion . . . . . . . . . . . . . . 5.3. Nuclear energy . . . . . . . . . . . . 5.3.1. Dual-use energy . . . . . . . . . 5.3.2. At the heart of nuclear fission 5.3.3. Developing nuclear fusion . . 5.4. New energies . . . . . . . . . . . . . 5.4.1. Hydroelectricity . . . . . . . . . 5.4.2. Wind energy . . . . . . . . . . .

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Chapter 7. Individuals and Society . . . . . . . . . . . . . . . . . . . . . . .

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7.1. Calculated choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. A question of style. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1. Assigning a work to its author . . . . . . . . . . . . . . . . . . . . . .

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7.2.2. Understanding a pictorial technique . 7.2.3. Discovering a personality type . . . . 7.3. The shape of a city. . . . . . . . . . . . . . 7.3.1. Transport . . . . . . . . . . . . . . . . . 7.3.2. Sound atmosphere . . . . . . . . . . . 7.3.3. Businesses . . . . . . . . . . . . . . . . 7.4. A question of choice . . . . . . . . . . . . 7.5. What about humans? . . . . . . . . . . . .

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Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Foreword Forms of Citizen Knowledge

For a long time, technology has served as a reference point in order to legitimize the notion of progress. Now, it is often seen as a deterrent. Technophiles and technophobes thus confront each other around the meaning to be given to technology in a sometimes dubious battle. Rather than imposing on technology a symmetrically inverse role as a sign of history or a sign of despair, it would undoubtedly be more beneficial for everyone to understand that technology does not exist in itself, that it is a political choice and deserves to be collectively reflected upon. In this case, while exploring the mysteries of mechanics, and consequently of scientific and technical knowledge, through the analysis of numerical simulation, the objective of Jean-François Sigrist, engineer and industrial researcher, is this: to rectify the mysteries created around the contributions of cutting-edge technological dynamics to contemporary research and to remind us that citizens have a certain power – that of the power of words that express choices – over scientists, experts and decision-makers. It is indeed with a mixture of cynicism and disbelief that many often react to statements about algorithms, for example, focusing media attention. Some talk about them in order to dominate the “ignorant”, others argue against seizing this mode of knowledge and conceptual construction by claiming its abstraction from the lived world and the last would like to push the “backward” to become “intelligent” by teaching them what they should know, based on this too ordinary sharing of the organization of the social world. It is clear that these three modes of approaching a hierarchical relationship between knowledge (scientific and technological) and people are based on the same presupposition: on the one hand there are “those who know” and on the other hand “the ignorant”. From the first to the second, the darkness of routine and superstition

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is invoked, which legitimizes their dominant position and their relationship with rulers. Jean-François Sigrist’s first concern is not to affirm doctrinally the validity of contemporary scientific and technological knowledge and approaches. Nor does he seek to maintain a classificatory pedagogical model, exposing only raw knowledge to those willing to learn. He encourages those who are ready to embark on the adventure to seek to understand what this knowledge means, taking into account the context in which it is advanced and the fictions with which they are confronted: cinema, drawing, painting, photography, etc. By facilitating the encounter with the uses of scientific and technological knowledge – objects used daily, simulation for industrial applications – within the culture of time, he interrupts the automatism of the social machine of knowledge that constantly divides the world between those who are “informed” or “cultivated” and those who are “behind”. In this respect, the spirit of this book is entirely woven from the relationships between the description of the mathematical and physical world as understood by knowledge and techniques and the deciphering of the specific cultural meanings that can be attributed to them. These meanings then refer less to games of optimism or pessimism or to functions of accompanying the educational order, or even to catastrophist speeches or a cautious morality of the slightest evil, than to the double exercise of the effort of scientific culture and the taking of political sides, to the benefit of all of society. Christian RUBY Philosopher

Introduction A Technology at the Service of Humans

In this second volume, we continue our discovery of numerical simulation technology, understood in a broad sense as a tool for carrying out virtual experiments. In the first volume, we have shown how the idea of representing a given entity in an abstract way is realized: a model made up of equations and/or data allows us to predict its evolution or behavior in different situations. Taking the example of mechanics in general, we first discussed various possible uses of simulation in the industrial sector and recalled its strategic nature. We then extended our presentation to other applications that require or perform simulations, such as artificial intelligence, which aims to simulate, in the sense of reproducing, certain human cognitive abilities. We concluded the presentation by questioning the meaning that numerical simulation can take and the techniques it helps to develop or whose advances it incorporates. The objective of this second volume is to provide some concrete answers to these questions by illustrating different fields of application of numerical modeling. Without claiming to be exhaustive in any way, we thus propose an overview of some of its uses in agriculture, the shipbuilding and aeronautics industry, earth and universe sciences, meteorology and climatology, energies, the human body and finally, we discuss the use of models covering certain activities of individuals, alone or in communities. This second volume, consisting of seven chapters, presents various contributions from researchers and engineers working in French laboratories, centers of expertise or industrial groups using numerical modeling to support their research and/or design work. Please note that any uncited quotations are taken from personal interwiews. We choose examples in these areas by showing how these digital techniques benefit humans, without avoiding the question of their use for other purposes.

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Faced with the difficulty of drawing clear boundaries between knowledge and skills, and between techniques, we have chosen to emphasize, with the variety of examples proposed, the links they maintain and the way in which digital technology contributes to changing scientific practices.

1 Agriculture

In 1916, Chicago, Bill was a worker employed in a foundry. Following an altercation, he fled the city, accompanied by his girlfriend Abby and his sister Linda. He found refuge in Texas where wheat was harvested from huge arable areas and a favorable climate allowed him to grow it. Hired as a seasonal worker by a wealthy farmer suffering from an incurable disease, Bill pushed Abby to give in to his employer’s advances. A calculation to get out of poverty? Set in a bourgeois house drowned in an almost endless expanse of wheat, inspired by the paintings of the American painter Andrew Wyeth (1917–2009), Days of Heaven (1978) recounts a psychological drama [MAL 78]. The contemplative camera of its author, the American filmmaker Terence Malik, also depicts the blazing sun of long working days, the power of harvesting machines and the hazards of harvests, stormy bad weather or locust invasion, which become a tragedy subject to the whims of the sky – whose unpredictability symbolizes that of human passion? Controlled and perfected for more than 10,000 years, as attested to by remains from ancient Egypt (Figure 1.1), agriculture remains a survival challenge for a humanity facing climate change in the 21st Century even though it is capable of changing its practices.

Figure 1.1. Cereal harvest, Tomb of Menna, Sheikh Abd el-Gournah Necropolis, Egypt (source: 10,000 Meisterwerke der Malerei, The Yorck Project)

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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1.1. Feeding the world Agriculture is also at the center of current ecological concerns and strategic issues, particularly those of state food sovereignty, to which simulation techniques provide answers. Today, the world’s cultivated land covers more than 50 million km2 (Figure 1.2): this area is about three times that of Russia, the largest country in the world with 17 million km2.

Figure 1.2. Allocation of land areas for food production (source: Our World in Data/https://ourworldindata.org/yields-and-land-use-in-agriculture). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 1.2.– Only 30% of the total area of our planet is covered by land, 70% of which is considered habitable (about 100 million km2). Humans use about half of it for agriculture, and less than one-tenth for urban infrastructure. More than three-quarters of the agricultural land is used for animal husbandry, combining land allocated to pasture and feed production (these aggregate data obviously do not reflect disparities between countries). The share of cultivated land has grown steadily for more than 10,000 years to meet the needs of a constantly growing world population. The latter was estimated at less than 1 billion people at the beginning of the 19th Century, reaching nearly 7 billion at the beginning of the 21st Century. In 2015, the four most populous countries in the world were China (1.4 billion), India (1.3 billion), the United States (305 million) and Brazil (201 million). Demographic projections estimate a world population of more than 11 billion people in 2100 (Figure 1.3).

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Figure 1.3. 1 World pop pulation growth h between 175 50 and 2015 and a projection ns to 2100 (sourrce: Our World d in Data/httpss://ourworldind data.org/world d-population-grrowth)

COMMEN NT ON FIGUR RE 1.3.– Sinc ce the 1970s, humanity as a a whole hhas been undergoing a demogrraphic transittion. The growth of the world populatiion is the b and deeaths. It is maarked by a siignificant result off the combineed effects of births increasee that commennced at the beeginning of th he 20th Centuury. It peakedd at more than 2% % in 1973 and has since decclined to 1.2% % in 2015. Demographic prrojections estimate it at 0.1% by 2100. Beehind this glo obal represenntation are siignificant c Povverty is the firrst factor delaaying the dem mographic differencces between countries. transition: the worldd’s least wealthy countriess are also thhose with thee highest population growth. The productive p cappacity of eachh country (Fig gure 1.4) depennds on soil quuality, the area avaailable or usedd for agricultuure, the climattic conditions to which it iss exposed and the available culttivation technniques and agrricultural pracctices developped there. d and partly reflectt the wealth off nations, While peeople’s lifestyyles are very disparate humanityy as a whole lives on creddit, consuming g resources att a faster ratee than the Earth cann provide.

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Figure 1.4. 1 Annual world w wheat yields y for 201 14, expressed d in tons perr hectare. Wheat iss the primary cereal c producced in the worl rld, aimed at both b human an nd animal and-landconsump ption (source:: Our World in i Data/https:///ourworldinda ata.org/yields-a use-in-ag griculture). Fo or a color ve ersion of this s figure, see www.iste.co.uk/sigrist/ simulatio on2.zip.

The American non-governme n ental organizzation Globaal Footprint Network O Dayy each year. The T latter corrresponds to thhe date of calculatees the Earth Overshoot the curreent year on whhich humanityy is supposed to have consumed all the rresources that the planet p is capaable of regenerrating in 1 yeaar. One of thee pieces of datta derived from thiss NGO’s calcuulations is thee number of pllanets Earth thhat would be nneeded to meet huumanity’s connsumption off renewable resources r in 1 year. By 22018, 1.7 planets Earth E are neeeded to suppoort humanity – and the exttrapolation off the data shows thhat the threshoold of two plaanets Earth will w be exceedeed well beforre the end of the firrst half of the 21st Century. Yet, in many Wesstern countriess, consumptio on and producction patterns lead to a duction (Figurre 1.5), show wing that significaant waste of food resourcces and prod humanityy has real rooom for maneuuver to changee its relationship with the w wealth of resourcees that the plannet that hosts it i still offers.

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Figure 1.5. Although edible, these tomatoes, produced in France, are discarded because they do not meet certain criteria based on the standardization of production and their packaging (source: © Jacques Péré, from the series “La Beauté du diable”, exhibition at the Galerie Lyeux Communs, Tours, June 2018). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip.

COMMENT ON FIGURE 1.5.– Nearly one-third of the food produced annually worldwide (1.3 billion tons) is destroyed or wasted. The leading position is occupied by fruits and vegetables. The amount of food lost every year is equivalent to more than half of the annual cereal production. Waste is higher in rich countries, where consumers throw away as much food each year as sub-Saharan Africa produces at the same time (more than 220 million tons). Food waste is observed at all stages of the food chain and concerns all actors: 32% is attributed to agricultural production, 21% to processing, 14% to distribution, 14% to collective and commercial catering and 19% to home consumption (sources: www.fao.org, www.ademe.fr). From the resources they consume, those from agriculture are among the most important for humans and the most strategic for States. During the 20th Century, advances in agricultural technology as a whole have generally reduced famine episodes whose causes are attributable to yield collapse [PIN 18b]. They have also been accompanied by irreversible environmental destruction, for example when new areas are being sought for intensive cultivation through massive deforestation. All over the world, some farmers are trying to renew current agricultural practices. Their credo is that more sober techniques can give as good results as those

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of intensive agriculture in particular, which consumes a lot of energy and water (Figure 1.6), and whose excesses are also increasingly contested [SOL 19]. “Nature has so much real wealth to unveil and humans have such a definitively superior potential for intelligence, that the combination of the two frankly gives hope [...] Working with nature and not against it, we realize that the solutions are there, before our eyes and that they often prove to be simpler and less costly in energy [...] We have divided by thirty our energy efficiency to produce food since the time of our grandparents... that sounds like a terrible insult to human intelligence” [ROS 18].

Figure 1.6. How thirsty is our food? (source: https://www.statista.com/chart/9483/how-thirsty-is-our-food/)

COMMENT ON FIGURE 1.6.– We use water in any productive activity, the amount consumed depending on two main factors: the climate of the production region and the agricultural practices developed there. For example, 35 L of water is needed to produce a cup of tea, 140 L for a cup of coffee, 75 L for a glass of beer and 120 L for a glass of wine; 2,400 L are consumed for the production of a hamburger, 40 L for a slice of bread and 13 L for a tomato (source: www.fao.org). In the 21st Century, will numerical modeling contribute to the development of agricultural techniques that ensure a sufficient level of agricultural production for all humanity and limit the degradation of its environment?

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1.2. Agriculture is being digitized In the richest countries, agriculture is becoming digital and modeling is a key focus of this change [WAL 18]. David Makowski, an expert in this field at INRA*, explains the objective: “Germany, Australia, France, Italy, the United States and the Netherlands are the pioneering countries in the use of numerical modeling in agriculture, recently joined by China. Numerical simulation makes it possible to assess the impact of agricultural practices, soil quality and climate on yields and the environment. The applications are varied and allow farmers, companies and public agencies to estimate the performance of different production methods in different situations. Despite the sometimes significant uncertainty of their simulations, models are frequently used to predict the environmental impact of agriculture by assessing the emissions of particulate matter, greenhouse gases or pollutants due to agricultural practices”. Numerical simulations in agronomy have used “mechanistic models” for two to three decades. These allow the functioning of crops to be described by means of equations; these, for instance, represent the production of biomass as a function of solar radiation, or the growth of plants as a function of soil temperature or humidity. Simulations make it possible to account for the physiological and biological dynamics of plants, on the scale of a plot or a set of cultivated lands. They can represent different agricultural practices and help to assess their impact on yields. An example of modeling applicable to biological phenomena? The interaction model between hosts and biological control auxiliaries. It describes how biological populations, such as predators and their prey (aphids and ladybirds for example), evolve in an ecosystem. For example, it explains the development cycles of many species (animal, plant, etc.) in many environments, such as the marine phytoplankton (Figure 1.7). The model consists of two differential equations, proposed independently by two mathematicians, the Austrian Alfred-James Lotka (1880–1949) and the Italian Vito Volterra (1860–1940), in 1925–1926. These equations are written as: ( ) ( )

=

( )−

( ) ( )

=− ′ ( )+ ′ ( ) ( )

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Numerical Simulation, An Art of Prediction 2

The equations describe the evolution of the prey and predator population, represented by variables ( ) and ( ). The first equation states that prey, having access to an unlimited source of food, would grow exponentially (this is rendered by the first term in the right-hand side of the equation ( )), and are sometime faced with predators at certain occurrence (this is rendered by the second term of in the right hand side of the equation − ( ) ( )). The second equation states that predators perish from natural death (this is rendered by the first term in the righthand side of the equation − ′ ( )), but grow by hunting prey (this is rendered by the second term of in the right-hand side of the equation + ′ ( ) ( )).

Figure 1.7. Satellite image showing algae growth in a North Atlantic region (source: www.nasa.gov). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 1.7.– In the waters of the North Atlantic, a large amount of phytoplankton, microscopic algae that play a role in the food chain of the marine ecosystem and contribute to the ocean carbon cycle, develops each spring and fall. The image is a photograph taken by NASA’s “Suomi” satellite on September 23, 2015. Blue spirals represent high concentrations of algae, waters loaded with microscopic creatures that contribute to the production of part of the planet’s oxygen. The Lotka–Volterra equations have as unknown the populations of the competing species, the coefficients describe their survival and mortality rates. They predict a cyclical evolution of populations that is consistent with the observations (Figure 1.8). Many other equation-based models are available for studies of organic and agricultural systems. In recent years, data-based simulations have been developed to complement these models – nowadays, they use methods such as automatic learning techniques, discussed in Chapter 4 of the first volume. Statistical models are based on an adjustment of equations to data and allow an empirical relationship between different quantities to be established.

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Fig gure 1.8. Typiccal evolution of o the prey/pre edator populattions as prediccted by the Lo otka–Volterra equations

Satelllites, drones (Figure ( 1.9), sensors, s field surveys: statisstical models are based on a largge number off data and it iss the variety and a diversity of the latter tthat gives credibilitty to predictioons. Data useed in statisticaal models are diverse: theyy describe the cropp environmentt (e.g. topogrraphy and meeteorology), farmers’ fa practtices (e.g. frequenccy of waterinng or spreadiing), animal species behaavior or plannt species growth.

Figure 1.9. Agriccultural droness are used to monitor m crops and collect usseful da ata to develop or validate ce ertain simulatio ons (source: © Christophe Maitre/INRA/w M www.mediatheq que.inra.fr/)

The models m of eacch family com mplement each h other, each providing infformation whose multimodel m anaalysis makes it i possible to identify i trendss [MAK 15]: “M Modeling is a synthetic exxpertise of th he knowledge available tto a com mmunity at a given time. One O of the mo ost promisingg approaches iis to reconcile these classes of models m with the statisticaal processingg of

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Numerical Simulation, An Art of Prediction 2

simulation data. The efficiency and reliability of ‘Big-Data’ techniques is increasing, and it is not excluded that they may eventually replace models based on equations...”. Simulations involve equations coupling different scales (plant, plot, farm or agricultural region). They require a large amount of data and still require very long computational times. Despite these current limitations, which artificial intelligence algorithms help to push back, modeling in agriculture is becoming more widespread and a tool for scientific debate and political decisions. Let us listen to the researchers involved in the development of models through a few examples. 1.3. Decision-making support Farmers, political and economic decision makers, and consumers shape the landscape of agricultural practices to varying degrees, each acting at its own level: by guiding a continental agricultural policy, by deciding to invest in a new machine tool, or simply by doing one’s shopping. Different agents, actors and practices influence it and the behaviors of each have societal and environmental consequences. Some agricultural practices have potentially negative impacts on climate and biodiversity, for example [BEL 19]. The disappearance of many insect species is attributed to the destruction of their habitat by intensive agriculture and their poisoning by the widespread use of pesticides [HAL 17, SAN 19]. How can these harmful effects be anticipated and limited? How can climate change be taken into account in current and future practices [BAS 14]? What is the best combination of agricultural practices that makes it possible to produce while guaranteeing a country’s food sovereignty? How can we legislate and cultivate for the benefit of the greatest number of people? Hélène Raynal, researcher at INRA and project manager of a digital platform dedicated to agrosystems [BER 13] provides an initial answer: “Different models aggregated within a shared computer system make it possible to represent agricultural systems taking into account their complexity. Modeling should be able to represent biological processes, such as plant growth. They must also make it possible to account for physical processes related, for example, to water (evaporation of water from the soil, drainage of water to the deep layers of the soil, etc.), carbon and nitrogen, which are the factors that determine agricultural production. They must also integrate the climate dimension or farmers’ practices (such as irrigation levels), and socio-economic aspects. These processes fit into different scale levels and, depending on the issue, the model is

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used to simulate a cultivated field, an agricultural operation – or even an entire region. The aim is to integrate as much relevant information as possible into the model, from soil chemistry to local climate factors, agricultural practices and assumed market trends or climate changes. Simulations make it possible to play on various scenarios and estimate the impact of a decision taken by stakeholders in the sector on agricultural production. They can also help to design new agricultural systems adapted to different issues, such as climate change and the reduction of chemical inputs to the crop”. This collaborative platform1 offers various services for the construction and computer simulation of models. In particular, it offers a range of mechanistic models produced by agronomists. Based on mathematical equations, they explain the biophysical and chemical phenomena involved in crop growth, the effects of bioaggressors or model economic balances. They are built separately by specialists in these different fields [RAY 18]. “In an overall simulation, it is a question of coupling different scales of description and reporting changes over time at the desired frequency (day, month, year), as well as in heterogeneous territories. When simulations aim to secure public actions, they focus on the country’s overall production. It is necessary to have a set of calculation points representing the different practices, which change according to the soil, the size and type of farms, the varieties grown and, of course, the weather conditions. Having data available to feed the models is a key point in the simulations”. The complexity of the different models used in interaction in a simulation leads to rather long calculations: performed on dedicated IT infrastructures, an overall simulation requires 2 days full of calculations and generates several gigabytes of data. The researchers’ experimental design is limited to half a dozen situations used to generate data for subsequent analyses. Scientists develop global indicators, reflecting the state of the system: they include soil quality, the yield of the territories observed (plot, farm and region), water (consumed, drained or irrigated) and nitrogen (consumed, drained or generated) cycles. Additional simulations on targeted areas allow the results to be refined. Together, they contribute to estimating the dynamics of the simulated systems, characterizing their agronomic interest and their environmental and economic sustainability (Figure 1.10). In some cases, simulation can help inform public decision-making, such as assessing the consequences of a public policy decision. 1 Available at: https://www6.inra.fr/record.

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The same approaach can be reeplicated at the t farm leveel to inform farmers’ w environm mental standaards and proofitability, choices. Combining compliance with nown to some farmers who may, for some prooduction systeems are efficiient and unkn various reasons, r hesitaate to adopt thhem. Christophe and Stéphane S Viggneau-Chevreaau are two winegrowers w from the o vines of abbout 30 hectarres in the Loire Vaalley [SIG 199]. They cultivvate parcels of Vouvrayy appellation. When W taking over the familly farm, foundded in 1875 annd run by four gennerations beforre them, moree than 20 yearrs ago, they decided d to connvert it to organic farming. It is i becoming necessary an nd obvious foor them to sttop using pesticidees, which alterr the soil in itts ability to reegenerate and deliver all itss minerals necessarry for viticultuure: “Foor the treatm ment of classiic vine diseases, we use contact prodducts sprayed on the grapes and eliminated e with water, witthout altering the hytosanitary products, whhich graain or taste of the winee. Unlike ph imppregnate the sap of the vine and are found... f even in the glass! In adddition, the usee of pesticidess depletes the soil: to comppensate, it is tthen neccessary to usee artificial yeeasts during vinification, v w which erases the aroomas and uniqueness of the soil”.

Figure 1.10. 1 Share off production alllowed by the ecosystem se ervices associiated with g grain maize cu ultivation [THE E 17]. For a co olor version off this figure, se ee www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 1.10.– This map, m based on o simulation results, showss that for grain maaize cultivatioon, about halff of the annual input requuirements of pplants are providedd by ecosystem m services andd therefore feertilizer inputss could be lim mited. The simulatioon work is parrt of the EFESSE study (Évaluation françaaise des écosyystèmes et

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des services écosystémiques). Launched in 2012 by the French Ministry of the Environment, the study aims to provide knowledge on the current state and sustainable use of ecosystems. The transition from their farm to the AB label, which warrants organic farming practices, was done at the cost of intense work: “The first three years, we gradually adapted our plots; this was accompanied by a drop in yield that was not immediately offset by an increase in quality. It took us about ten years to ensure a quality and performance that we consider satisfactory!” More than 20 years ago, this mode of production was not understood. At the beginning of the 2000s, it became a guarantee of quality and consumers were not mistaken, meeting the offer proposed by the two brothers and by other producers in their region. Their bet proved to be a win–win situation for all. Models developed by researchers in digital agriculture can support the decision and transition required by such reconversions (Figure 1.11). Hélène Raynal explains: “Models contributing to decision-making are a delicate matter. They reproduce, at the farm level, the calculations made, for example, for the whole country in the context of public policies. Including detailed data – such as the equipment available for irrigation or exploitation, crop organization and location on the land, possible polyculture rotations, cohabitation with livestock, etc. In addition, the models also seek to capture farmers’ preferences: the risks they are willing to take in their investments, the balance they want to favor between short- and long-term productivity, the time they spend at work and how they can integrate environmental issues”. Simulations are carried out on the plots and make it possible to develop an overview of everyone’s practices. By enriching them with climate change data, they offer farmers the opportunity to anticipate some of their consequences in the long term. “The criteria for analyzing simulation data are developed with the farmers involved in the process: this joint approach is essential to ensure its relevance and quality. While the most traditional indicators are those of investments and returns, operators also include those of quality of work, such as the possibility of taking days off... This criterion is, for example, a determining factor in the choices of certain operators – and it is highly contextual”.

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Num merical Simulatio on, An Art of Prrediction 2

Manny professionaals are on thhe lookout for f new practices and thee models proposedd by researcheers give them the means to make m profitabble decisions.

Figure 1.11. Working hours (perr ha and pe er year) requ uired by a fa armer for on (yellow squ uares) and pe esticide-free p production “conventtional” agriculttural productio (orange triangles), as part of a durum whea at and sunflo ower crop ro otation, in AY 17]. For a color versiion of this fig gure, see ww ww.iste.co. southwest France [RA uk/sigristt/simulation2.zzip.

NOTE.–– Statistical models m to preddict yields. Compllementing or replacing equuation-based modeling, statistical modeels allow yield projections p of new crops. A protein-rich legume l the planting of whicch allows crop rootation does noot require nitrrogen fertilizerrs and offers to t diversify prroduction; soya iss the subject of o European agronomic a stu udies, while itts production is largely carriedd out in other continents, c Noorth America and a Asia in paarticular.

Fig gure 1.12. So oya is a legume valued for itts nutritional qualities and w whose inte ensive cultivattion in some parts p of the wo orld also has a negative influ uence o the environm on ment (source:: www.123rf.co om)

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Where to grow soybeans s in Europe? Following whhich practicees (using phytosanitary produucts whose haarmful effects on the enviroonment are feeared... or by meaans of organicc farming)? What W are the expected e yieldds? How could climate changee affect its im mplementation? Numericaal modeling helps h to answ wer these questioons, as Nicolas Guilpart, ann agronomy researcher, expllains: “D Data-based modeling m explloits the statiistical relationnships between yields recordeed in regionss of the worrld and clim matic conditioons p Such h modeling uses automattic reecorded durinng growing periods. leearning techniiques and charracterizes eco ological nichess, the regions in w which a culturee can potentially develop”. Perform mance data foor soybeans, or any other crop, around the world caan predict areas suitable s for cultivation c in other region ns, whose clim matology – aand other factorss, such as soill quality – aree similar. Bassed on global data, the prediction is still lim mited to regionns the size off a French dep partment. The models also rreveal the likely evolution e trennds of these arreas with climaate change.

Figure e 1.13. Calcula ation of whea at crop yields in France and d worldwide: tthe figure represe ents yield incrreases estimated by statistic cal methods, in i different co ountries of the wo orld and for the e French depa artments. The e unit is the ton of wheat pe er hectare cultivatted and per ye ear [MIC 13]. For F a color ve ersion of this fiigure, see ww ww.iste.co. uk/sigrrist/simulation2 2.zip.

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1.4. Environmental impact Fertilizers are organic substances, of plant or animal origin, or mineral substances (synthesized by the industrial fixation of atmospheric nitrogen) intended to provide plants with nutrient supplements. They contribute to improving their growth and increasing the yield and quality of production.

Figure 1.14. Fertilizers promote plant growth but their overintensive use has long-term harmful effects on the environment or may be dangerous for human health (source: www.123rf.com/)

COMMENT ON FIGURE 1.14.– Often used in a mixture, fertilizers are mainly composed of three elements: nitrogen contributes to the vegetative development of all overground parts of the plant, phosphorus strengthens their resistance and participates in root development, and potassium promotes flowering and fruit development. They also provide plants with complementary elements (such as calcium or magnesium) and trace elements (such as iron, manganese, sodium or zinc), useful for plant life and development. Their use dates back to the early days of agriculture and, nowadays, the development of the chemical industry encourages their use, sometimes to an excessive extent. Their widespread use worldwide (Figure 1.15) supports the yields expected by some farmers, often at the expense of soil, water and air quality. Used in excessive quantities, fertilizers are responsible for the depletion, or even destruction, of ecosystems – inhibiting the ability of soils to regenerate naturally or permanently polluting groundwater reserves.

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Figure 1.15. 1 Global usse of nitrogen, potassium and phosphate e fertilizers worrldwide in 2014: major m agricultu ural countriess are making g massive use u of fertilizzers. The quantitie es used are expressed e in kilograms k perr hectare of cultivated c land d (source: Our Wo orld in Data/h https://ourworld dindata.org/fertilizer-and-pe esticides). Forr a color version of o this figure, see s www.iste.co.uk/sigrist/s simulation2.zip p.

Sophhie Génermonnt, a researchher at INRA,, has been working w for m more than 20 yearss on the devvelopment of a platform for f simulatingg ammonia eemissions resultingg from the usse of fertilizerrs [GEN 97, RAM 18], which w contribuute to the degradattion of air quaality: “Forrmed from orgganic nitrogenn, ammonia iss a pollutant of o the air, andd after depoosition, of sooils and wateer. About 95 5% of anthroopogenic amm monia (pressent in the envvironment thrrough human action) comes from agricuulture. My work w on the formation f andd volatilization n of this com mpound is baseed on data measuring its i concentraations in plan nts, water or soil. Thesee are p ical and bioloogical compplemented byy models of thhe physical, physico-chemi processes at differrent scales”. The platform p deveeloped becausee of the work carried out ovver more thann 20 years by varioous research teams is iniitially dedicaated to liquidd organic maanure. Its functionalities are exxtended in ordder to apply the modelingg to mineral ffertilizers 1 and to stuudy pollution ddue to the [CAD 044] and thickerr organic fertillizers [GAR 12], use of certain c plant protection prroducts [BED 09]. It is allso used to aassess the

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consequences of certain livestock practices – which are also responsible for high nitrogen emissions [SMI 09]. Models are carried out for a plot, a small agricultural region, a country, or even, in the long term, a continent! They take into account the various factors that influence the migration of ammoniacal nitrogen in the environment – and exploit the data that make it possible to characterize it: meteorological, geological variables for the composition of surface soils, physical and chemical variables for the composition of fertilizers, statistics for the input practices carried out by farmers. “The simulations consist in solving equations modeling the physical, physicochemical and biological phenomena at work in soils, and at the interface between the soil and the atmosphere. Carried out on a plot scale, they give very fast results: a few seconds of calculation give an idea of the evolution of the phenomena that can actually be observed over a few weeks and this at an hourly time step!” Many physical processes are modeled by equations that form the basis of the models used in the simulations of changes in chemical species concentrations. These include the laws established in the 19th Century by the French physicist Jean-Baptiste Biot (1774– 1862), the French engineer Henry Darcy (1803–1858) and the German physiologist Adolf Fick (1829–1901). They relate the flow of a physical quantity to a variation of another quantity: – the law described by Fourier and formulated by Biot reflects the diffusion of heat. It is written as follows ϕ = −λ∇T and stipulates that the heat flux (ϕ) flows from hot areas to cold areas (∇T), all the more easily as the medium in question is conductive (λ); – Darcy’s law expresses the flow rate of an incompressible fluid filtering through a porous medium. It is written as follows ϕ = K∇H and indicates that the flow of a fluid between two points, made by its flow (ϕ), is all the easier as the medium is porous ( ) and that the resistance to its flow, expressed by the hydraulic pressure losses (∇H), is low; – Fick’s law accounts for the diffusion of matter. It is written as follows ϕ = −ρD∇c and indicates that a chemical species spreads from areas where it is highly concentrated to areas where it is less concentrated. The mass flow of a component (ϕ) is inversely proportional to changes in its concentration (∇c) and depends on its density (ρ) and its propensity to spread (D). The calculation algorithms consist of solving these equations, to which are added, on the one hand, those of the physicochemical equilibria between the different species in play present in the gaseous, aqueous state, or adsorbed on clays and organic matter of the soil (highly dependent on temperature, soil moisture and its acidity), and, on the other hand, those making consumption and/or production effects by biological reactions linked to the presence of microorganisms. Physicochemical models make it possible to calculate the

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evolution of chemical concentrations in the different soil layers, and in particular at the surface. Volatilization is then calculated by using equations describing the convection and diffusion effects of gaseous ammonia from the ground surface to the atmosphere based on the effects of wind conditions and stability of the lower atmospheric layers. Box 1.1. Physicochemical equations

A set of simulations, aggregated for different plots and taking into account composition differences as well as meteorological factors, allows data to be reproduced on larger scales – typically a small agricultural region. “It is possible to scale up, for a country, with the same principle: by performing as many simulations as necessary to describe an entire region and synthesize the results of the calculations. No less than 150,000 simulations are needed to represent the use of mineral and organic fertilizers during the soil fertilization phase (in the fall and then from February to late spring) and estimate their effects on the scale of a country like France. Two days of calculation on about forty cores are necessary to realize it!”. NORD PAS-DE-CALAIS 51.2 HAUTE PICARDIE NORMANDIE 88 CHAMPAGNE 54.3 ARDENNE BASSE LORRAINE 129.7 NORMANDIE 82.5 ILE-DE-FRANCE 53.8 44.4 BRETAGN E 83.8

PAYS DE LOIRE CENTRE 178.6 BOURGOGNE 84.3 101.1

NORD PAS-DE-CALAIS 8.7

ALSACE 21.8

FRANCHE COMTE 31.3

POITOU CHARENTES 105.1 AUVERGNE LIMOUSIN 42.3 RHÔNE-ALPES 21.8 58 AQUITAINE MIDI 79.5 PYRENNES LANGUEDOC PROVENCE ALPES ROUSSILLON CÔTE D'AZUR 86.9 12.8 9.9

(a) Use of nitrogen fertilizers

BRETAGNE 25.4

HAUTE NORMANDIE PICARDIE 18.8 CHAMPAGNE 8.4 ARDENNE LORRAINE ILE-DE-FRANCE 29.8 13.8 6.6

BASSE NORMANDIE 13.4

PAYS DE LOIRE 14

CENTRE 32.1

ALSACE 3.5

FRANCHE BOURGOGNE COMTE 11.6 4.7

POITOU CHARENTES 23.8

AUVERGNE RHÔNE-ALPES LIMOUSIN 5.8 8.6 2

AQUITAINE 15.4

MIDI LANGUEDOC PYRENNES ROUSSILLON 17.7 3

PROVENCE ALPES CÔTE D'AZUR 2.7

(b) Ammonia emissions

Figure 1.16. From the use of nitrogen fertilizers to ammonia emissions in France [HAM 14]

COMMENT ON FIGURE 1.16.– The figure on the left represents the quantities of nitrogen used in agriculture in France during the 2005–2006 crop year in the form

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of ammonia and urea and therefore susceptible to volatilization (the values are expressed in thousands of tons of ammoniacal nitrogen). The figure on the right shows the resulting ammonia emissions (values are expressed in thousands of tons of ammonia, NH3). The choice is made here to present the results of the calculations for the entire season, according to the different regions of the country and for the two main categories of fertilizers: synthetic fertilizers (in gray) and organic waste products (in black). The difficulty of the calculation lies in the reliability of the data required to inform the model: composition of the fertilizers used, types of fertilized soil, crop species and the fertilization routes preferred by farmers, including dates, doses and forms of fertilizer applied and methods of application. “Simulations allow us to identify interesting trends. Their quality depends very much on the quality of the data on which they are based. Soil type, range of inputs, emission data and field surveys are the preferred sources for researchers to inform their models. The validation of the calculations continues to pose problems: although the simulations are able to report the concentration of ammonia in the air with good spatial and temporal resolution, we do not currently have such an accurate measurement network to directly compare the results of our calculations with field observations – this is a current area of research involving different teams in France”. The researchers’ calculations tend to reflect the variability of the situations encountered through sensitivity studies: their analyses are being refined and are providing decision-makers with tangible evidence for assessing the risks associated with the massive use of fertilizers and, in the near future, phyto-pharmaceuticals. NOTE.– At the heart of the matter to understand soil chemistry. For the American physicist Richard Feynman (1918–1988), simulating the world asks us to account for the mechanics of the infinitely small: “Nature isn’t classical, damnit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy” (quoted by [BAI 16]). This idea was followed by two researchers in theoretical physico-chemistry, Fabienne Bessac and Sophie Hoyau, in order to study the mechanisms of pollutant adsorption in soils [BEL 17a, BEL 17b]: “Atrazine is an herbicide whose marketing and use have been banned in France since September 2002 and June 2003, respectively. However, they are still found in groundwater in some regions today.

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Our research aims O a to undeerstand the ph hysico-chemiccal mechanism ms thhat would exxplain how thhe soils exposed to it releease it into tthe w water...”.

Figure 1.17. 3D reprresentation of atrazine (sourrce: www.com mmons.wikimedia.org). on of this figurre, see www.is ste.co.uk/sigriist/simulation2 2.zip Forr a color versio

COMMENT ON FIGUR RE 1.17.– C8H14ClN5 is the raw chemica al formula for atrazine, the active ingrediennt of a pesticcide, also listted, accordingg to the Inteernational mistry nomencclature, as 2-chloro-4-(ethyylamine)Union of Pure and Applied Chem 6-(isoppropylamine)-s-thiazine. Thhe figure reprresents a 3D view of the molecule and hig ighlights the atomic a bonds between hyd drogen (H, in white), carboon (C, in black), nitrogen (N,, in blue) andd chlorine (Cll, in green). Atrazine A is a powerful herbiciide that hass long been appreciated by some faarmers becauuse it is inexpennsive and quuite powerful. It was bann ned in France in 2003 annd in the Europeean Union beccause of its addverse effects on health and the environment, but is still used today in some countriies, such as the United Statees. It is att the atomic scale that sccientists are trrying to undeerstand the ddesorption phenom mena – the mechanism m by which molecules adsorbedd on a substraate detach themseelves from it. The model used is grad dually being built to desccribe soil compoosition, includiing water and pesticide. “W We built a moodel by takingg into accountt the pesticidee alone and then thhe pesticide inn interaction with w different elements preesent in the sooil, suuch as sodium m Na+ and calccium Ca2+. Th hen we added clay and finallly w water. At each step, we were w able to observe the differences in innteractions annd understandd the phenom mena involvedd, in particullar how the bindinng sites betweeen the pesticcide and the clay c involved in d chaange at the mo olecular scale””. abbsorption or desorption

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Num merical Simulatio on, An Art of Prrediction 2

Simulaations consist of solving thhe Schrödingeer equation (C Chapter 1, V Volume 1) and caan be used too achieve therrmodynamic quantities forr the chemicaal species being modeled. m Thiss is one of thee most accuratte models imaginable for thhis type of problem m – and it is also a one of thee most time-co onsuming. The caalculations proovide access too two types off information: – Abbsorption enerrgies and the position p of ato oms in the corrresponding structures: the low wer the total ennergy of the calculated c stru ucture, the morre likely it is tto exist; – Chhanges in the spatial s organizzation of atom ms over time, over o very shorrt periods of time, in the ordder of the fem mtosecond to the nanosecoond (10−12 annd 10−9 s, respecttively), can prrovide thermodynamic inforrmation on the studied system.

Figu ure 1.18. Exam mple of calcullation at the attomic scale [B BEL 17b]. For a color version off this figure, se ee www.iste.co o.uk/sigrist/sim mulation2.zip

COMMENT ON FIG GURE 1.18.– The figure represents a molecular structure calculaated for the innteraction betw ween atrazinee and clay. Thhe soil is moddeled here by an infinite crystaal lattice: in practice, it is i a cell, on the t edge of w which are appliedd conditions of repetitivveness, refleccting an inffinite extensiion. The calculaation shows how h the atrazzine moleculee behaves in this environm ment and

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what the associated energies are. The simulation allows us to find the most probable structures after the adsorption of the pesticide on the clay. “Due to the complexity and size of the models, we used HPC calculation methods. Simulating the desorption of the pesticide in water requires, for example, nearly two million hours of calculation – spread over the thousands of cores of a supercomputer!” Calculation at the atomic scale is a first step in research: it serves as a reference for validating models that introduce simplifications and lend themselves to faster calculations. The objective is to carry out simulations under environmental conditions, with the data collected in the fields. Calculations using these models, in which accuracy is demonstrated by comparison with the atomic scale calculation, should determine the pesticide partition constants between the liquid and mineral phases – and answer the initial question. It is a wonderful problem, because it is far from simple! 1.5. Plant growth Vegetation is one of the crucial resources for humanity, providing it with food and energy – and in some cases a place to live. Satellite observations help to consolidate plant occupancy data on the planet’s surface (Figure 1.19). They enable scientists to understand the influence of natural cycles on vegetation (such as droughts or epidemics) or that of human activities (such as deforestation or CO2 emissions).

Figure 1.19. Vegetation map obtained from satellite observations (source: NASA/www.nasa.gouv). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 1.19.– The shades of green on the map correspond to values ranging from 0.0 to 1.0, in arbitrary units. Values close to 1.0 (dark green) indicate the presence of abundant vegetation, as in the Amazon rainforest. Values close to 0.0 (beige) indicate areas with little vegetation, such as the oceans or the Arctic continent. Forests cover 30% of the world’s land area, equivalent to just under 40 million km2, while treeless vegetation (tundra, savannah, temperate grasslands) occupies about the same area. In 1985, English filmmaker John Boorman recounted in The Esmerald Forest how a world disappears, the world of the Amazon rainforest tribes [BOO 85]. The son of an engineer who oversees the construction of a gigantic dam is taken from his parents by a tribe of Forest Men. As the dam’s construction was completed, the father and son found themselves in circumstances that led them both to confront progress and humanity. The dam will eventually give way under the waters of a river doped by torrential rain, engulfed by the songs of frogs calling on the forces of nature. The engineer who wanted to destroy his work to protect the future of his son and that of a tribe wishing to live in peace will not have this power. The Amazon rainforest is still one of the largest plant communities on the planet today. According to FAO2 estimates, it is now disappearing at an average rate of 25,000 km2 per year (equivalent to half the size of Austria) to make way for new crops. At this rate, it will have completely disappeared by the first half of the next century. It pays the highest price for the consequences of human activities: more than half of the world’s deforestation. The evolution of vegetation as a whole is of particular concern because of its dual importance: it supports a large part of biodiversity and contributes to the absorption of atmospheric CO2. Analyzing satellite observation data, NASA researchers show that in just under 20 years, the planet has re-vegetated with an area equivalent to that of the Amazon, with India and China being among the main contributors to this trend. The observed vegetation corresponds, on the one hand, to the growth of new forests, contributing to the sequestration of carbon from the atmosphere, and, on the other hand, to an extension of agricultural areas, whose natural carbon storage balance is generally neutral [CHE 19]. Understanding the growth mechanisms of species continues to occupy scientists. In the first half of the 20th Century, the British biologist d’Arcy Thompson (1881– 1946) became interested in the shape and growth of living organisms, publishing his thoughts in an exciting collection [THO 61]. He looks for invariants and universal principles that govern the evolution of life – for example, fractal structures or particular sequences (Figure 1.20).

2 Data available at: http://www.fao.org/forestry.

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Figure 1.20. The Fibonacci spiral: a model (too simple?) to explain plant growth (source: www.123rf)

COMMENT ON FIGURE 1.20.– Leonardo Fibonacci (1170–1250) was a 13th Century Italian mathematician. The Italy of his time was a region formed by scatterings of merchant cities in strong competition (Venice, Pisa, Genoa). Trade activities needed numbers and calculation to support their economic development. The mathematician developed algebraic methods to contribute to this. In particular, he drew inspiration from Indian and Arab mathematics, while Roman numerals, still widely used in Europe, forced calculation in a rigid numbering system that the invention of zero helped to loosen. The sequence that bears his name is defined from two values, then each term is calculated as the sum of the two previous ones. Thus, starting from 1 and 1, the terms are 2, 3, 5, 8, 13, 21, etc. This sequence, which has properties of interest to mathematicians, is found in some natural growth mechanisms. The Fibonacci sequence hides the famous golden number Φ = (1 + √5)/2. Discovered in the 3rd Century BC by Greek mathematicians, Φ seems to be present behind the architectural choices made in antiquity, for example in the construction of the Parthenon in Greece. “Let no one ignorant of geometry enter” is the motto of the Academy, founded in Athens by Plato in the 4th Century BC. The Platonic school makes mathematics one of the instruments of the search for truth. To this is added that of harmony, whose golden number is the hyphen. Φ is the Greek letter traditionally used to designate it and it also refers to philosophy. For very different reasons, the golden number fascinates human beings who sometimes tend to find it everywhere even where it is not [LIV 02]. Created at the initiative of the Royal Botanical Garden of Edinburgh, the website The Plant List3 aims to provide an exhaustive list of the various plant species: there 3 Available at: http://www.theplantlist.org/.

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are currently more than 1 million. Nature is characterized by a great variability of shapes (Figure 1.21): how can we accurately model the development of such diverse plants?

Figure 1.21. Variety of leaf shapes (source: www.123rf/Liliia Khuzhakhmetova)

Since the late 1960s, scientists have been using a formalism that is particularly well suited to modeling plant growth. It finds its roots not in the field of mathematics but in that of grammar! Frédéric Boudon, a researcher at CIRAD*, is an expert in these tools, the so-called “L-systems”: “The L-systems were introduced in the late 1960s by Hungarian biologist Aristid Lindenmayer to describe some of the processes encountered in biology. They are particularly effective in modeling plant development and are based on the rules of ‘formal grammar’. These can provide a realistic account of the influence of the plant’s architecture, vitality and environment on its growth”. In an L-system, a plant is represented by a sentence whose elements, or modules, themselves symbolize the components of the plant (stem, branch, flower, leaf, etc.). A set of rules governs the dynamics of these modules: they formalize biological processes and model plant transformations. The production of a new element (leaf, flower, fruit), growth or division of an existing element (stem, branch) are therefore represented by sentence equivalents of our language, which itself has its own syntactic rules (the order of words in a sentence) and is based on a given semantics (a set of words).

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Figure 1.22. Weeds generated by a three-dimensional L-system program (source: www.commons.wikimedia.org)

COMMENT ON FIGURE 1.22.– The rules implemented in the L-systems seek to represent the living: the probability of regrowth of a cut part, the amount of biomass produced, the birth and hatching of a flower, the production and ripening of a fruit. They can take into account environmental factors: amount of light received, level of sugar reserves, concentration of a hormone, etc. They make it possible to arrive at a very realistic modeling, a genuine digital plant! “The validation of models is done by comparing them with the dynamics and patterns observed in the field. There are no specific restrictions on the use of L-systems and researchers can therefore treat any type of plant: grasses, plants, trees! Their architectures can be reproduced in a very realistic way, including at fine detail levels. By using so-called ‘stochastic approaches’, it is possible to reproduce by simulation the heterogeneity observed in nature. Different biophysical phenomena such as branch mechanics or their reorientation towards the sun or as a function of gravity can be included in these simulations”. While they formalize the understanding of plant growth through simple mathematical rules, L-system-based models allow different types of applications such as yield prediction. The challenge in this case is to have models interact at different scales in order to obtain an overview: from plants or planting groups, to the plot and the entire farm. This is a vast field of research in digital agriculture. Modeling by L-systems already contributes to the evaluation of certain techniques,

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such as agro-ecology, which are receiving increasing interest due to the growing awareness of ecological issues and the need to preserve the emerald forest? NOTE.– Growing plants “in-silico” with L-systems. The typology of a plant, the phenotype, results from the expression of its genetic heritage (its genotype), and its interactions with the characteristics of the environment in which it develops (its environment). These interactions largely determine biomass production: reconstituting the phenotype of plants is therefore a key-factor in calculating the yield of a production. Artificial intelligence techniques based on deep learning from imaging data can contribute to this objective by automatically and quickly performing repetitive tasks such as counting sheets. In the learning phase, it is necessary to have a database large enough to make the algorithms efficient, which is not always the case in agronomy! The databases that can be used are generally limited and campaigns to enrich them are very expensive. One solution proposed by some researchers is to generate digital plants by simulation: the variety of forms produced thus enriches existing databases at low cost (Figure 1.23).

Figure 1.23. The virtual plants (left), obtained in silico by means of L-systems, have similar characteristics to the real plants (right), obtained in vitro

COMMENT ON FIGURE 1.23.– The efficiency of the L-systems is such that researchers show that the simulations are able to produce a variability in the

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characteristics of synthetic plants close to that of real plants – otherwise the data used by the learning algorithms would not be of good quality. The researchers even demonstrate that the latter learn, with similar effectiveness, either from real data or from data produced by synthetic models [UBB 18]. Let us conclude this chapter with the understanding that, in general, agricultural modeling addresses three scientific issues: – understand and predict plant growth processes; – assess the impact of agricultural practices in ecological and economic terms; – informing the policies of decision makers and farmers’ choices. They are thus becoming an essential tool for agricultural research, meeting the vital needs of humanity in the 21st Century: feeding populations and preserving their environment.

2 Aiir and Maritim M e Transsport

At itts height in thhe 2nd Centuury, the Romaan Empire extended over tthe entire Mediterrranean region. Land and seea routes ensu ured the dominnation of Rom me, which derived its wealth from f the expploitation of the resourcess of the terrritories it ontinental meeans of transsport, the controlleed. Supportedd in particulaar by interco globalizaation of trade,, initiated in antiquity, a inten nsified in the 20th 2 Century to a level probablyy never seen before b in humaan history (Fig gure 2.1).

Figurre 2.1. To whicch countries does d the world d export? (sourrce: Observattory for Econom mic Complexitty/www.atlas.m media.mit.edu u). For a color version of thiss figure, see www.iste..co.uk/sigrist/s simulation2.zip p

COMMEN NT ON FIGURE E 2.1.– In 20 017, world tra ade representeed $16.3 trilllion, with exportations to Europpe accounting for 38% of th he total amount, to Asia 377% and to a and Germanny were the top three North America 18%. The United States, China N 90% of o world trad de was carriedd out by sea, with 9.1 importinng countries. Nearly billion toons of goods trransported on ships sailing across the oceeans.

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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2.1. The long march of globalization The current globalization is the result of a period of intensive exploration of the Earth undertaken by Europeans between the 15th and 17th Centuries. European expeditions helped to map the planet and create maritime trade routes with Africa, America, Asia and Oceania. In 1492, the Italian navigator Christopher Columbus (1451–1506), financed by the Spanish monarchy, crossed the Atlantic Ocean and reached a “New World”: America, named after the navigator Amerigo Vespucci (1454–1512), who understood that the lands discovered by Columbus were indeed those of a new continent. In 1498, the Portuguese navigator Vasco da Gama (1469– 1524) led an expedition establishing the first maritime link with India by sailing around Africa. Explorations to the west and east continued with the Portuguese Ferdinand Magellan (1480–1521) who performed the first circumnavigation of the Earth in 1522. This first globalization is leading to some of the most significant ecological, agricultural and cultural changes in history. European exploration ended in the 20th Century, when all the land areas were mapped. At the end of the 18th Century, when the shipbuilding techniques of the time were recorded in works that reflected the latest knowledge in the field (Figure 2.2), a technological revolution began: humans realized Icarus’ ancient dream!

Figure 2.2. Taken from the work of Édouard-Thomas de Burgues, Count of Missiessy, Stevedoring of Vessels, published by order of the King, Under the Ministry of Mr. Le Comte de la Luzerne, Minister & Secretary of State, having the Department of Marine & Colonies. In Paris, from the Imprimerie Royale, 1789 (source: personal collection).

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In 1783, the French inventors Joseph-Michel and Jacques-Étienne Montgolfier (1740–1810 and 1745–1799) developed the first hot-air balloon capable of carrying a load through the air. The first flight demonstration of the hot air balloon took place in Versailles in September 1783 in front of King Louis XVI. A sheep, a duck and a rooster were the guinea pigs on this balloon trip1. The first balloon flight piloted by humans dates back to November 1783: the French scientists Jean-François Pilâtre de Rozier (1754–1785) and François-Laurent d’Arlandes (1742–1809) became the first two aeronauts in history. Despite its imposing mass, nearly a ton, the balloon designed by the Montgolfier brothers took off from the Château de la Muette, on the outskirts of Paris. It landed in the middle of the city some 25 min later, after reaching an assumed maximum altitude of 1,000 m and traveling about 10 km. Aeronautics then developed because of the work of the British engineer George Cayley (1773–1857) who understood the principles of aerodynamics and designed the first shape of an aircraft. The invention of this word is attributed to Clément Ader (1841–1925), a French engineer known at the time for his work on the telephone. In October 1890, he succeeded in making the first flight of an aeroplane carrying its engine and pilot. “Éole”, his aeroplane, was inspired by the flight of storks and bats. It was powered by a propeller driven by a twin-cylinder steam engine. The German engineer Otto Lilienthal (1848–1896) then carried out numerous flight experiments on small gliders and understood the importance of designing curved wings. The Americans Orville and Wilbur Wright (1871–1948 and 1867–1912) designed small planes on which they perfected their flight control, going from about 10 seconds and a few meters for Orville in 1903 to more than 2 hours and several hundred kilometers for Wilbur in 1908. In France, the United States, England and Denmark, the public was fascinated by the exploits of the pioneers of aviation. The first continental and maritime crossings followed one another: the French Louis Blériot (1872–1936) crossed the English Channel in 1909, the American Charles Lindbergh (1902–1974) the Atlantic in 1927. The First and Second World Wars accelerated the development of aeronautical and naval technology. Aircraft were equipped with weapons and contributed alongside submarines to intelligence, convoying and offensives. The aircraft carrier allowed squadrons to be projected beyond the land and the naval air forces played a decisive role in the Second World War [ANA 62, BAY 01, SMI 76]. After 1945, the military and civil construction industries developed jointly and today, air and sea transport evidence record traffic (Figure 2.3): nearly 50,000 ships 1 Animals contributed just like humans to the exploration of the skies: in the 20th Century, the Russian dog Laika was the passenger of the spaceship Sputnik 2; her stay in space in November 1957 preceded, by a few years, that of Yuri Gagarin (1934–1968) who became, in April 1961, the first human in space.

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carry 900% of the gooods traded eveery year worlldwide, whilee some 100,0000 flights carry moore than 3.5 biillion passengers.

(a)) Maritime trafffic (source: www.shipmap.o org)

(b b) Air traffic (so ource: www.th heguardian.com) Figure 2.3 3. Visualization n of maritime and a air traffic. For a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip

Aircrraft and ships also reach new w transport caapacities: – In 2005, Airbuus completed the first flig ght of the A380, A the larggest civil passengeer aircraft in service. s Four years y later, Aiir France operrated the aircrraft’s first commerccial flight betw ween Paris annd New York [MOL [ 09]. Poowered by fouur engines

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and equipped with a double deck, the A380 can carry up to 850 passengers at nearly 1,000 km/h over a distance of 15,000 km2; – In 2018, the French shipping company CMA-CGM welcomed the “Saint Exupéry” [STU 18], a freight ship built by Hanjin Heavy Industries and Construction in the Philippines, into its fleet. It is 400 m long, it can reach more than 20 knots and carries a cargo of 20,600 TEU (arranged end-to-end, the containers it ships form a chain of more than 123 km)3. There are many issues involved in the design of ships and aircraft. It is a question of manufacturers guaranteeing ever-increasing performance – in terms of safety, speed, silence, service life, energy consumption, comfort or environmental impact – posing ever-increasing innovation challenges for engineers. Without claiming to be exhaustive, as the subjects are so varied, this chapter proposes some examples where numerical simulation accompanies engineering studies in shipbuilding and aeronautics and where it contributes to improving performance. 2.2. Going digital! The America’s Cup is one of the oldest sailing yacht competitions. Since the end of the 19th Century, it has seen international teams compete against each other. Traditionally raced on monohulls, it also gives space to multihulls. Catamarans that are lighter and lighter, with thin lines and dynamic hulls, literally float above the water. Saving themselves from friction, much more significant on water than in air, they reach ever higher speeds! This innovation was partly made possible by simulations in fluid mechanics (Box 2.1), of which the Swiss physicist and mathematician Daniel Bernoulli (1700–1782) was one of the pioneers. In particular, he understood that, in a fluid flow, acceleration occurs simultaneously with the decrease in pressure and proposed an equation to account for this observation. This

2 However, the A380, which has been in service with many international airlines since its entry into service, has not been able to consolidate its place in the air in the long term, perhaps a victim of its size. In 2019, due to the lack of a sufficiently large order book, Airbus announced that it would cease production of this non-standard aircraft [JOL 19]. 3 The baptism of the “Saint Exupéry” in 2018 was accompanied in France by particular questions on the environmental impact of maritime transport, in a context where the sector remained one of the last outside the Paris Agreement of 2015. It should be noted that in 2018, the 174 Member States of the IMO (International Maritime Organisation, dependent of the United Nations) agreed on a quantified objective to reduce greenhouse gas emissions, aiming to reduce them by half by 2050 [HAR 18].

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physical property is used by engineers to design aircraft wings, propellers, wind turbines or hydrofoils for the catamarans used in offshore racing.

Figure 2.4. Flow calculation around a lifting profile (source: Naval Group). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.4.– The shape of the foils allows a flow of water or air to be separated at the leading edge, before joining at the trailing edge. The fluid flowing on the upper part of the foil, the “suction side”, travels a greater distance than the fluid flowing on its lower surface, the “pressure side”. According to the law established by Bernoulli, the accelerated flow on the upper surface exerts a lower pressure on the profile than that of the slowed flow under the lower surface. This pressure difference generates a force on the foil: hydrodynamic lift. The lift flow calculation shown in the figure indicates how the water flow flows around the hydrofoil (white lines). It also highlights the regions of overpressure (low-velocity regions in green and blue) and depression (high-velocity region in red) responsible for the lift. The lift created by the movement of air or water allows an aircraft to fly, a propeller or sail to propel a ship, or a wind turbine to recover wind energy. With a proper curvature and an adequate inclination of the foil on the hull, the lift exceeds the weight of the ship and it can almost fly. The challenge is then to optimize the shape of the foil, in order to achieve the best possible separation of the flows at the leading edge, to ensure their reattachment at the trailing edge and to limit the pressure fluctuations generated by turbulence phenomena in the flow. An art, permitted for more than two centuries by the Bernoulli equation. Useful for understanding fluid physics, however, this equation is too simple to help engineers in their design tasks. Nowadays, they use more complete models that accurately represent fluid dynamics. To this end, they resort to the power of computers to represent hydrodynamics and understand it by means of a calculation. Naval designers and constructors are increasingly using numerical simulation to propose new shapes or materials for hulls, sails or any important part of the sailboat.

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However, it is necessary to choose the most efficient ones so as to achieve the expected performance in the race: material resistance, flow understanding, hydrodynamic, and aerodynamic performance, as with these flying yachts. These innovations pave the way for other applications in naval architecture and the computational techniques that can assist designers are varied. They use generalist tools, such as tools more specific to the sail design profession, for example (Figure 2.5).

Figure 2.5. Simulation of the aerodynamics of a sail (source: image owned by TotalSim/www.totalsimulation.co.uk)

The sailboat’s speed prediction is based on different calculation techniques. Starting from a given architecture (rigging, platform, appendages, etc.), it is a question of finding the best possible adjustments to the sailboat (heading, speed, etc.) in order to achieve the highest speed under the assumed sea conditions (in particular the speed of sea and air currents). The simulation is based on an experiment matrix defining the different possible configurations and the associated calculation points. The adjustment of a foil or appendage explores a thousand configurations. The data are calculated in about 10 days. They are then analyzed using advanced algorithmic techniques to determine an optimal setting. Simulation makes it possible to identify general trends that are useful to designers and contribute to a sensitivity analysis. It is a matter of sequencing the architectural parameters that have the greatest influence on a given ship’s behavior. Benjamin Muyl, consulting engineer, indicates the direction of the next innovations in this field: “Tomorrow, the simulations will also take on the wide-open sea: from static (where sea and wind conditions are frozen), the simulations will become

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dynaamic. The aim m will be to propose behaavioral models that evolve over time. The applicaations envisaaged are num merous, from the crew traaining mal control. The T latter allows better addjustments in very simuulator to optim criticcal race phasees, such as the passage of bu uoys, where thhe slightest taactical errorr can be difficult to catch upp!” Whatt is the next horizon h for thhe simulations? Real-time models! Integgrated on board shhips, they assisst the sailors involved i in th he race or assiist the skipperrs in their choice of settings at seea.

Figure 2.6. 2 Simulation of possible routes for an n offshore racce (image ma ade using Neptune e code, routin ng software developed d by Xavier Pillon ns; source: BM MD/www. www.bm muyl.com). For a color ve ersion of this figure, see www.iste.co.uk/sigrist/ simulatio on2.zip

Enginneers anticipate a converrgence betweeen scientific computing and new techniquues, such as daata learning. Everything E rem mains to be im magined and buuilt and it is a new direction thatt simulation iss taking in maany other fieldds. As in oceaan racing, t developmeent of new geeneration simuulations are varied and the road choices for the u Chhance is part of ship racinng, and fortunnately has carry theeir share of uncertainty. little to do with technnology! So may m the best (and ( luckiest)) skipper winn the next w or withoutt the invisible help of algoriithms. race... with

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Two boats tossed by the impetuous flow of an ocean whose excessive waves lick the sides of a steep coast. This is a print by Japanese artist Katsushika Hokusai (1760–1849) – Chôchi in Shôshu province – made between 1832 and 1834 [HAA 14]. In the foreground, a fishing boat, governed by the steady hand of a man who seems used to harnessing the power of the flows. He is propelled by three rowers, their backs bent with their effort – a sign of respect for the force of Nature? In the background, another boat slides across the sea. A blue wave squanders its energy on a reef: waterfalls, sea spray and drops of salt. This print depicts humans – both fragile and courageous as well as ingenious in adversity – confronted with forces beyond their control: those of hydrodynamics. Hokusai was a contemporary of the century that saw the development of modern fluid mechanics. Understanding and modeling fluid dynamics begins in particular with Bernoulli’s work; that Leonard Euler used in order to establish the flow equation of a perfect and incompressible fluid. The French Claude Louis Marie Henri Navier (1785– 1836) and the English Gabriel Stokes (1819–1903) then generalized this equation to a viscous fluid flow. They write the conservation of physical quantities within it: the mass and the momentum – the product of mass by velocity. The Navier–Stokes equation, which deals with the conservation of the momentum, takes the following form: +

∙∇

=

− ∇ + μ∆

Involving the speed and pressure in the fluid, as well as its physical characteristics (density ρ and viscosity μ), it is another writing of Newton’s second law of motion and reflects the dynamic equilibrium of the fluid. Its acceleration, written to the first member of the equation, is caused by mechanical forces of different kinds. The external forces are gravity (g, first term of the second member) or result from pressure variations (−∇p, second term of the second member). The latter indicate that a fluid flows from areas of high pressure to areas of lower pressure. When the fluid is viscous, the friction between the fluid layers produces a force represented by the third term of the second member (μ∆v). Acceleration results from variations in time and space of velocity. Therefore, the first member of the Navier–Stokes equation has two terms: the first describes the evolution of speed over time (∂v/ ∂t), whereas the second accounts for the evolution in space (v ∙ ∇v). The viscosity of the fluid characterizes the intensity of friction within the fluid – that is, its tendency to stick to the walls that channel its flow. The Navier–Stokes model assumes that the deformations of a fluid’s volume are proportional to the variations in its velocity. Such a fluid thus reacts immediately to the forces that set it in motion and is also the site of friction. Physicists call such a fluid Newtonian, as are water and oil, for example. This model does not describe all types of flow, far from it! Let us run on a sandy beach with the tide rolling in: the wet sand offers resistance to our jerky steps. On the other hand, let us press our foot down gently, and we sink into it like dough. The flow of wet sand depends on the force applied to it and works in a very different way from water: it is non-Newtonian. Many fluid foods, such as mustard, mayonnaise or chocolate, are

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also similar (Figure 2.7). Their behavior is sometimes surprising, even annoying, like ketchup stuck in its bottle and pouring capriciously onto our plate! Simulations of nonNewtonian fluid flow pose real difficulties for engineers and constitute a current field of research, meeting the needs of the food industry, for example.

Figure 2.7. Chocolate is a non-Newtonian fluid (source: www.123rf.com/kubais) While the complexity and beauty of flows is accessible to everyone at a time of contemplation by the sea, lake or river, it has long fascinated artists and scientists, most notably the Italian Leonardo da Vinci (1452–1519). One of his drawings, sketched toward the end of his life, depicts an elderly man in a contemplative attitude, along with sketches describing the complexity of a water flow by bringing it closer to that of hair (Figure 2.8).

Figure 2.8. Old man contemplating the flow of water, drawing by Leonardo da Vinci, circa 1503 (source: Royal Collection Trust – © Her Majesty Queen Elizabeth II 2019) Da Vinci is attributed this metaphorical description: “Observe the movement of the water surface, which resembles that of a hair, which has two movements, one caused by its weight, the other by the direction of the curls: so the water has swirling movements, one part due to

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the main current, and the other to a random and reversed movement” (quoted by [LUM 97]). The detailed observation of physical phenomena contributes to their modeling and offers to follow in the footsteps of great minds. Let us look at a flow, like Leonardo. Its speed varies more or less strongly over time: all you have to do is focus your attention on one point and watch the water flow evolve. Is it peaceful and regular? It is then said in physical language that it is “stationary”. Is it changing, alternating moments of high and low flows? It is then qualified as “unsteady”. The velocity (or flow rate) of the flow varies over time; it also varies in space. If we focus on another location, there is a good chance that the flow does not have the same characteristics. When a leaf falls into the water, the flow rocks it as it changes. The same happens with petals or pollen, physical bodies of variable size, set in motion as the wind blows: fluid physicists speak of “advection”. When a chemical, such as a dye, marries with water, it mixes more or less slowly with it, until it merges completely with it: this mechanism is called “diffusion”. Diffusion and advection also combine and contradict each other, to become “convection”. A stone on the watercourse constrains its passage. This presence is not insignificant: it is a source of flow modification, as is the weight of the water that carries it to a lower latitude. Fluid physicists use an equation describing these physical phenomena. For a characteristic flow quantity (water or air velocity, concentration of a chemical, temperature, etc.), an equation expresses the principle of its conservation:

Each of the terms reflects an effect described above. The first term of the first member reflects the unsteadiness, and the second describes advection. The first term of the second member describes the sources and the second term describes diffusion. The Navier– Stokes equations transcribe these physical phenomena for an incompressible fluid flow. Depending on the conditions, flows have very different characteristics (Figure 2.9). In particular, they can be laminar (fluid layers slide over each other due to the viscosity of the fluid and vortices of identified and predictable size can be observed) or turbulent (fluid layers mix strongly, giving rise to vortices of varying sizes and random evolution). The Navier–Stokes equation contains the physics of turbulent flows.

Figure 2.9. A flow from the laminar state (left) to the turbulent state (right) [YIV 15]

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Turbulence is a complex phenomenon, marking a regime with wide spatial disparities and unpredictable fluctuations over time. It has always intrigued physicists and mathematicians, as these words attributed to the British physicist Horace Lamb (1849– 1934) testify. Author of a treatise on hydrodynamics (still read today by engineers and researchers in fluid mechanics), he speaks of turbulence as follows: “I am an old man now, and when I die and meet God, there are two things I would like to be enlightened on. One is quantum (mechanics), and the other is the turbulent flow of fluids. And about the first one, I’m rather optimistic...”. Reporting turbulent phenomena in a simulation is common to many fields using fluid mechanics, with the following limitation: beyond a certain observation time, it is no longer possible to guarantee that the calculated solution is valid. This is one of the reasons why the prediction horizon for meteorological simulations remains limited to a few days. The first scientific classification of turbulent flows is proposed three centuries after da Vinci’s observations. It is the result of experiments by the Irish physicist Osborne Reynolds (1842–1912). In 1883, he identified different fluid movements using an experimental device. Based on his work in fluid mechanics, a number bearing his name makes it possible to classify flows according to common physical phenomena (Figure 2.10).

Figure 2.10. Observation by Osborne Reynolds on flows [REY 83] COMMENT ON FIGURE 2.10.– Using an experimental device, Osborne Reynolds studies the flow of a colored fluid through a tube. His experience allows him to visualize the structure of the flows under different conditions, by varying the speed of the fluid. At low speed, the layers of fluid regularly slide over each other by rubbing and adhering to the wall: this is the “laminar” regime. By gradually increasing the velocity, Reynolds finds that the fluid behavior is more irregular, the flow becomes “turbulent”. He shows that the transition between the two regimes occurs for values very close to a number without a physical unit. He writes it down , where denotes the diameter of the tube, is the speed of the fluid, and and are the density and viscosity of the fluid. This number, named in his honor, is denoted as . It is one of the most employed in fluid mechanics since the Irish engineer’s experiments. The Reynolds number makes it possible to relate

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identical flow patterns, which occur on objects of very different sizes. Fluid physicists speak of “similarity”. This ensures that data collected on a small-scale device can be used to predict flow characteristics around a large-scale object. This makes it possible, among other things, to use test facilities and obtain accurate and reliable data for many other configurations. At the same time, the Dutch painter Vincent Van Gogh (1853–1890) was inspired by the traces left by physical phenomena before his eyes. His painting transcribes the forms of movement: some of his paintings represent landscapes with tormented skies and fields, composed of swirling clouds and vegetation swept by the winds. Toward the end of his life, Van Gogh, then interned in the asylum of Saint-Rémy de Provence, contemplated from his room the dynamics of celestial whirlwinds. He painted Starry Night (1889), one of his most famous artworks. Some scientists claim that the painter was able to transcribe with acuity certain structures observed in turbulent flows. At the beginning of the 20th Century, the French photographer Etienne-Jules Marey (1830–1904) devoted three of the last years of his life to documenting the movements of the air; the images he had produced still retain great esthetic and scientific value (Figure 2.11).

Figure 2.11. Triangular prism presenting one of its bases, Etienne-Jules Marey, 1903, photograph (source: Collection La Cinémathèque française)

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Marrey paved thee way for maany scientists for many deccades who woould use visualizzations to underrstand fluid phyysics. In 1982, the American researcher Millton Van Dyke (11922–2010) pubblished a book of some 400 black and white photographs p [D DYK 82]. An Albbum of Fluid Motion M tells thhe story of thee diversity andd beauty of thee flows: nowadaays it could eqqually be founnd in the Finee Arts or Scieence departmennts of a bookstoore. Van Dyke obtained photoographs from sccientists aroundd the world enggaged in fluid mechanics researrch: these photoographs bear wiitness to the maany researches tthat have helped to identify diifferent phenom mena, such ass wave movem ments or sounnd wave propagaation. Turrbulent flows arre marked by thhe existence off eddies of varyying scales. Larrge ones transport the kinetic energy e of the fluid, f small onees dissipate it by b friction, thee process ending when those sm mall enough to dissipate d energy y as heat are reaached. This meechanism was prooposed in 1922 by British matthematician and d meteorologistt Lewis Fry Ricchardson (1881–1953). In 19411, the Russiann mathematiciaan Andrey Kollmogorov (19003–1987) completed Richardsonn’s description by establishing g equations describing the inteensity of large-sccale movementss and the evoluttion of the size of dissipative scales. s observations give Richardson and Kolmogorov’s K g substancee to algorithms which accountt for turbulencee in numerical calculations. c Th he Direct Numerical Simulationn (DNS) of turbulence thus coonsists of solving the Navierr–Stokes equattion with all sscales of turbulennt eddies. It thherefore requirees very fine ressolution and coomputational tim mes that are quickly becomingg beyond the reach r of engineeers and researrchers. The coomputing power of computers is constantly increasing, however, h it is estimated thaat direct simulations of turbulennt flows on largge objects (e.g.. wind turbines, trains, planes or ships to scalee) will not be avvailable to enginneers until 2050 0. Particular coonfigurations, obbjects of a relatiively moderatee size compareed to the size of the eddies to be calculaated, are neverthheless suitable for f DNS calculaation of turbulen nce (Figure 2.12).

Figure e 2.12. Flow calculation c aro ound a bearing g profile with tu urbulence reso olution. Forr a color versio on of this figurre, see www.is ste.co.uk/sigriist/simulation2 2.zip

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COMMENT ON FIGURE 2.12.– The calculation is intended to represent the development of turbulence around a hydrodynamic profile in order to understand how it influences fluctuations in lift force. At the leading edge of the profile, on the bottom left, the flow conditions are known: turbulence is statistically represented with a given energy. The simulation makes it possible to report on its evolution around the two sides of the profile (the upper left and lower right top surfaces). It identifies the areas of strong fluctuations at the trailing edge, top right (source: Antoine Ducoin, École Centrale de Nantes). Developed over several decades, approaches other than direct simulation make it possible to cover many industrial needs. A first alternative is to model, totally or partially, the turbulence. The proposed principle corresponds to the observations: in some flow regimes, an overall movement is observed and fluctuations around this mean are observed. This is the starting point for average turbulence modeling (or RANS* – Reynolds Average Navier–Stokes). To this end, fluid physicists use a decomposition of velocity into an average field and a fluctuating field. It takes the so-called “Reynolds decomposition” and is written as: =

+ ′

where refers to the average value of the speed and ′ is the fluctuation around this average value. The written conservation equation for the average velocity is then of the form: +

∙∇

= −∇ + ( + ′(v′))∆ +

This is identical to the original Navier–Stokes equation, with the following exception: turbulent phenomena are modeled by a dissipation mechanism of the average velocity. The latter is represented by the turbulent viscosity: noted ′(v′) in the equation, it depends on speed fluctuations. An equation is associated with the latter, expressed as turbulence kinetic energy. The parameters of this equation are based on empirical data, valid for simple configurations, such as flow on a flat, large surface. The simulations performed with RANS turbulence modeling require lower spatial resolution and are therefore faster than DNS – but sometimes prove less precise. In cases where engineers want to access more accurate flow data without direct simulation, they use a hybrid approach. This consists of solving the large scales of turbulent flow and modeling the smaller scales: fluid physicists speak of Large Eddy Simulation (LES*) [SAG 98]. Calculation with turbulence modeling (RANS) is fast but only gives access to average flow values. It provides precise results for estimating, for example, the lift of an aircraft or the hydrodynamic resistance of a ship to its advance in water. The calculation with resolution of large eddy turbulence (LES) takes longer to be performed. It produces

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accurate data to estimate, for example, pressure fluctuations in a flow that cause unwanted noise or vibration in many situations (Figure 2.13). While waiting for direct simulations of turbulence, researchers are improving the accuracy of the calculation models, mainly by exploring two main paths: – the first is based on physical models that seek to represent specific phenomena. Resulting from observations, numerical or experimental, their analysis is translated into equations that are further solved using a numerical method; – the second uses various mathematical methods, in particular those of data analysis, to provide an abstract representation of phenomena. The data come from experiments, numerical or physical, and may benefit from automatic learning techniques.

(a) Calculation with average modeling

(b) Calculation with resolution of large scales

Figure 2.13. Examples of hydrodynamic calculations around a hull appendage (source: Sirehna/Naval Group). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Among the many methods that can be used to calculate a solution to the equations stating the conservation of mass, momentum and energy in a fluid, the finite volume

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technique is one of the most efficcient. It is imp plemented in many m fluid meechanics calculattion codes. Let us describe its principle very briefly. b Wriitten on a giveen volume of flluid, the conserrvation equatioon makes it possible to formalize a balance: the t quantity enttering and leaviing a volume inn a time of obsservation compennsates for its variation v (its disappearance orr creation). Fluuid physicists sstate this balancee in a general eqquation written as: Ω +

v∙n Γ=

Σ Ω+

Λ

dΓ Γ

This equation conntains, in this order, the contributions of all flow mechhanisms: unsteaddiness, advectioon, the contribuution of sourcees and diffusioon. It is writtenn on all volumees that are consstructed by the mesh of the do omain in whichh the flow is siimulated (Figure 2.14). On each volume, the quantity of intterest and its vaariations are caalculated from thhe values at speccific points.

Figu ure 2.14. Mesh hing of the fluiid in finite volu umes around an a aircraft (so ource: www.blog.p pointwise.com m). For a color version of thiss figure, see www.iste.co o.uk/sigrist/sim mulation2.zip

As discussed in Volume V 1, the validity of thee simulations is based in parrt on the theoretiical results estaablished by matthematicians. However, H engineeers do not yet have all the maathematical resuults to the equuations used in n their fluid mechanics m calcuulations. Indeed, Navier–Stokess equations stilll challenge math hematicians to this t day: demonnstrating propertiies of existencee, uniqueness – and especially regularity – to their solutions remains one of the scientific challenges c of thhe 21st Century y. In 1934, the French mathem matician Jean Leeray (1906–19998) established theoretical resu ults giving valiidity to the sim mulations perform med by engineeers. In 2017, tw wo American researchers r prooposed a demonnstration indicatiing that solutions obtained diggitally – as currrently calculateed by engineerrs – may

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not cover all observable physical phenomena [BUC 17]. Their mathematical results suggest that there are several possible solutions to the Navier–Stokes equations. One of them establishes, for example, that a fluid at rest can be animated, after a certain time, by a spontaneous movement. This result goes against the physical observations and the first principle of mechanics stated by Isaac Newton. Mathematicians show that the corresponding solution is very irregular. The physical interpretation that can be proposed is that the corresponding fluid movement is so erratic that it is zero on average. The fluid remains very still in the eyes of physicists. If mathematics predicts several possible states of a physical system in a given situation, some may not have any concrete meaning. The dialogue between mathematics and physics is thus at the heart of certain paradoxes that are sometimes dizzying. As with instrument vibrations, modal analysis of fluid flows provides an understanding of the physics of turbulence (Figure 2.15). The modes of a flowing fluid are hidden in the Navier–Stokes equation and various algorithms may be used to calculate them.

Figure 2.15. Modal analysis of a flow [KAR 18]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.15.– The figure shows three modes of a supersonic gas flow. The jet is located on the left edge of the image. The flow modes correspond to a particular organization of its energy. They are represented in terms of velocity intensity, as the maximum values in the red (positive velocity) or blue (negative velocity) zones.

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Modal analysis allso makes it possible p to imp plement simulaations based onn model reductioon* techniquess, representing only those modes m that have the most siggnificant contribuution to flow ennergy (Figure 2.16).

(a) Comple ete flow calculation

(c) Calculatio on with a mode

(b) A mode m of flow

(d) Calculatio on with five mod des

Figurre 2.16. Calcu ulation of wate er flow downstrream of a cylin nder with a reduced orde er model. For a color version n of this figure e, see www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEENT ON FIGURE 2.16.– 2 The firstt calculation prresented in the figure f is based on a socalled “high-fidelity” “ s simulation. It is i performed with a complete flow model annd serves as a ref eference since it i contains all the physical inf nformation for this configurattion. The flow heere consists of vortices due too the fluid deta aching at the cylinder c wall. T The flow modes correspond c to an organized structure s containing a certainn amount of eneergy. An algorithhm makes it poossible to extraact the most sig ignificant modees (in terms off energy) from the simulation daata. The one-moode model is too o simple to desccribe the flow pproperly. With fivve modes, the accuracy of thhe reduced-ord der model is eqquivalent to thaat of the complette model, whichh requires the equivalent e of sevveral thousand modes. Sim mulations basedd on “massivvely parallel” algorithms caan also help perform calculattions on compleex models. Thuus, with an HPC C simulation, engineers produuced data to evaluuate the safety of o a 200 m longg frigate subjectted to the impacct of a 20 m higgh wave. Such a simulation waas carried out in 2008 (Figu ure 2.17) and involved i signifficant IT resources. Simulation allows virtual experiments, e wiithout risking a crew and it exxtends, in its way,, Hokusai’s artiistic representattions.

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Figure e 2.17. Simulation of the wave surge on a frigate (sourcce: calculation n carried out by HydrrOcean/www.h hydrocean.fr) COMMEENT ON FIGURE 2.17.– 2 How to design d a ship and a ensure that its crew will bee able to navigatte safely, in diff fficult sea condiitions or during g sensitive operrations? As empphasized in Voluume 1, the enginneers of the 21sst Century have at their dispoosal the experieence and know-how of those who preceded them m, their physica al sense and thee sum of their ttechnical knowleddge. Other toolls are also avaailable, those off numerical sim mulation [BES 006]. For this sim mulation, the hearts h of a thoousand computters had to beaat in time in oorder to producee, from a num merical model containing c seveeral million unnknowns, a set of data which proved p useful too naval architeccts. Box 2.1. Navier–Stokes N s equations

2.3. Opttimum desig gn and prod duction 2.3.1. Lightening L th he structure es Com mbining properrties of both riigidity and lig ghtness, compposites are inccreasingly used in many industtrial sectors, particularly in aircraft, space, s automootive and m contrribute to the sttructural weight reduction oobjectives shipbuildding. These materials set by manufacturers m in order to reeduce operatin ng costs – in particular p thosse of fuel consumpption. Pascal Casari, an exxpert in composite materialls at the Univversity of Nantes, tells t us: “Aeeronautics is the industrrial sector th hat most sysstematically uuses com mposite materrials. Long beefore the birth h of large airccrafts, such ass the A380, these matterials were chhosen in the design d of aeroobatic planes,, for g adoppted which weight gaain is crucial! Other sectorrs have then gradually m: the autoomobile andd shipbuildin ng industries nowadays use them

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com mposites to deesign many parts, p some off which contrribute to essenntial funnctions, such as a structural inntegrity”. A coomposite is a heterogeneoous material, obtained byy assembling different componeents with coomplementaryy properties. Generally made of fibbers, the reinforceement of the composite ennsures its mecchanical strenngth, when thhe matrix, most oft ften a thermooplastic or thhermosetting resin, allowss the cohesioon of the structuree and the trannsmission of forces to thee reinforcemeent (Figure 2..18). The structuree is then orgganized into laminated fo olds that connstitute thin sstructures particulaarly suitable foor high-perforrmance applications.

Figure 2.18. Example of a composite ma aterial: a multiilayer (source: ns.wikimedia.o org). For a collor version of this t figure, see e www.common www.iste.co o.uk/sigrist/sim mulation2.zip

“Coomposite moodeling poses many chaallenges for researchers and enggineers in mechanics m andd materials science. s Obtaained by various proocesses (weavving of fibers, injection of resin, etc.), thhey are produuced by injection or foorming and may m contain deefects: they aree thus media w with ‘inhhomogeneouss’ (they vary from one poiint to anotherr of the part) and ‘annisotropic’ (thhey depend on the direection of strress) mechannical prooperties. Thus, the mechaniical strength criteria c valid for homogeneeous andd isotropic materials, m suchh as metallicc materials, are a generally too connservative for composites”. Afterr decades off using criteeria based on “material strength” [T TSA 08], mechaniical engineers are now deveeloping criteriaa that are bettter able to reprresent the damage mechanisms of o composites. “Too that end, it is thus necesssary to better calculate the internal crackking at the t folds or at a the interfaace between the t folds, leadding to the w wear mechanisms callled ‘delaminnation’ and to t model thee effects of the mperature or humidity) h on their t ageing”. envvironment (tem

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Com mposites simulation is used by engineers with two maain objectives,, explains Christopphe Binétruy, modeling m expert at the Écolle Centrale dee Nantes: “Nuumerical moddeling makes it i possible to carry out reall ‘virtual testss’ in ordder to determinne by calculaation the mech hanical properrties of materrials, succh as their riggidity or theiir resistance to t different thhermomechannical streesses. Calculaations give enngineers the ability to ‘diigitally’ desiggn a matterial, whichh will then be develop ped to obtaain the dessired chaaracteristics foor a given prroduct or use.. Simulations are also usedd to opttimize manufaacturing proceesses: designin ng a mold, dim mensioning a tool or anticipating a thhe formation of o defects are among the reesearch objecttives now wadays”.

(a) Resin R injection n simulation [COM 05 5]

(b) Calcullation of the mechanical m beh havior of a “honeycomb” struccture (source: EC2 Modéliisation/www.ec2-modelisatio on.fr)

Figu ure 2.19. Num merical simulatiion for composites: manu ufacturing proccesses and mechanical prop perties. For a color version of this figu ure, see www.iiste.co.uk/sigrrist/simulation2 2.zip

COMMEN NT ON FIGUR RE 2.19.– Numerical N sim mulation helpps to undersstand the mechaniisms of impreggnation of a fibrous fi networrk with a resinn (left). Startinng from a known arrangement a o fibers, chaaracterized exxperimentally by means off imaging of tools, it is possible to predict by caalculation how w the fluid occcupies the voluume at its disposal,, as a functtion of its innjection ratee and rheologgical properrties. The simulatioon is based, for fo example, on o highly visco ous flow equaations, describbed by the “Stokes model”, or on o flows in porous p media, described byy the “Darcyy model”. p herre uses the SP PH particle meethod [MON 888], other While the calculation presented s as finite elements, are also effectivve for perform ming this numericaal methods, such type of simulation. s T models caan be refined The d to take into account the chemical transform mations of thee resin duringg cooling and d solidificationn, which are ddescribed by therm mal and therm modynamic eqquations. The overall mechhanical properrties of a

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composite material can also be calculated. The figure shown on the right details a calculation of the mechanical strength of a honeycomb composite structure. This type of simulation makes it possible to predict the characteristics of the part to be built with this material – the remaining numerical calculations to scale one, for large objects, is still not very accessible due to modeling costs and calculation times. Simulations require real expertise in data specification, interpretation of results and overall calculation management: it is generally performed by experts in the field. “Calculation to the scale of the material is still a necessary step: with composites, it is difficult to deduce the characteristics of a structure from those of a tested specimen. In addition, gathering the geometric and physical properties of composites remains very tedious: these can be obtained reliably at the cost of expensive tests. Since the latter also present a very high variability, simulation appears to be an effective tool for quickly assessing the consequences of this variability on the properties of the material”. With composites, numerical simulation contributes to the development of materials science. Enabling the design of parts with the qualities expected for industrial uses, it requires us to think at the same time about the product to be manufactured and the desired characteristics of the material which it will be made of. Beyond the product and the material, it is also developing in order to understand and optimize manufacturing processes. 2.3.2. Mastering processes In the shipbuilding industry, as in other mechanical engineering industries, welding is a widespread operation (Figure 2.20).

Figure 2.20. Welding operation (source: www123rf.com/Praphan Jampala)

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For instance, a frigate hull is made of metal panels on which stiffeners are welded to ensure its resistance – to difficult sea conditions as well as to different types of attacks (explosions and impacts). Tens of thousands of hours of welding time are required to build a ship. The process uses a wide variety of techniques and sometimes welders work under difficult conditions, for example in areas of the ship where access is difficult. Mastering welding techniques requires long experience that must sometimes be adapted to a new construction. The metal is heated at the weld point and it deforms: over large dimensions, this residual deformation can even be observed with the naked eye. Under the effect of the heat imposed at the time of welding, the metal is also transformed. It is under tension, like skin that heals. The residual stresses should be as low as possible so as not to reduce the overall strength of the ship hull. Deformations or residual stresses are sometimes too high: this non-quality of production can weigh heavily on the production costs of a series of vessels, partly because straightening deformed shells or repairing some welding areas is time consuming. Florent Bridier, numerical simulation expert at Naval Group, explains how modeling can be used to understand welding: “Numerical simulation of welding helps to optimize the process (the sequencing of the passes, or the pre- or post-heating phases), or to validate the repair techniques. At stake: avoiding thousands of extra hours of work at the shipyards, which justifies assessing the value of this technique in order to modify and optimize certain welding operations”. Welders and researchers share their knowledge of the process and its abstract modeling: their practices are mutually beneficial. The simulation may be based on a so-called “multi-physics” model to account for the complexity of the phenomena involved in welding. In order to obtain the most accurate simulations possible, it is necessary to describe: – the supply of heat, and possibly of material, by the welding process used, as well as its diffusion in the concerned area. It can be carried out in several steps, which the simulation will take into account; – the transformations of the matter undergoing these thermal effects. The structure of metal crystals is influenced by temperature and in turn changes the mechanical properties of the material (such as its strength, ability to absorb or diffuse heat, etc.); – the mechanical behavior of the metal in the area where it melts, as well as the deformations and stresses it undergoes.

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These physical phenomena are coupled in the sense that one influences the other and vice versa (Figure 2.21). A direct simulation of welding quickly becomes very costly in terms of modeling and calculation time, especially for real configurations. Instead, it is used on simple geometries, representing a specific area of a ship. The complete multiphysical calculation performed on a T-joint shows the temperature distribution in the joint and reports the formation of the weld seam (Figure 2.22). It provides accurate data on the operation. These are used on a simpler model at the scale of a hull panel. The simulation allows us to choose a welding sequence that limits residual deformations. The use of such calculation is twofold: – assist welders in adjusting process parameters (e.g. size and intensity of heat source); – produce a digital database for different shapes of welded joints, according to different processes used. These data are then used in simplified models, allowing calculations at the scale of the welded panels.

Figure 2.21. The thermal, mechanical and metallurgical phenomena involved in welding are coupled and simulated together

COMMENT ON FIGURE 2.21.– The temperature (T), thermal conductivity (λ), phases (α) and deformations/stresses (ε(u), σ(u)) in the metal are the physical quantities to be calculated. They depend on each other: the accuracy of the model depends on the representation of all these effects in the calculation.

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(a) T-join nt

(b) Hull H panel

Figurre 2.22. Numerical simulatio on of welding (source: ( Naval Group). For a color t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip version of this

To be accurate andd reliable, thee simulation uses the metal characteristicc data and c with temperature t o in the crysttal state. Thesse data, obtainned at the or how it changes cost of expensive e expperimental cam mpaigns, consstitute a real asset a for the coompanies or laboraatories that prooduce them. NOTE.–– Non-destrucctive testing annd numerical simulation. Non-deestructive testting (NDT) iss a set of meth hods allowingg us to characterize the integritty of structurees or materialls without deg grading them. They are widdely used in induustry in geneeral, and in shipbuilding and aeronauutics in particcular, for example to check the quality of the parts produced, too ensure theiir proper functiooning or to antticipate futuree repairs. The soo-called “ultraasonic inspecction method”” (Figure 2.233) is one of the most commoon NDT methhods. It consissts of emitting g acoustic wavves and deteccting their interacctions with thee material, whhich makes it possible to iddentify defectts present in the part. p The re-em mitted waves,, like an echo,, are then convverted in real time into a digitaal image of thhe defect, thus located and characterized. c Designning an ultrasoonic inspectioon device poses many challlenges (optim mizing the design of the senssors, choosingg the approp priate frequenncy for the materials inspectted, calculatinng the optimall inspection trrajectories, etcc.) that researcchers and engineers identify ussing digital sim mulation. Benoitt Dupont, NDT T ultrasound expert e at CET TIM* [DUP 100, DUP 14], teestifies to this: “We are a solicited by b our industrrial customers (in energy, transport, m mechanical engineering) to carrry out inspectiions of parts, machines andd installationss. We use

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simulaation to suppoort the design of a control method. It alllows us to chhoose the process best suited to t the geometrry and material of the part to be inspecteed, and to preparee the inspectioon session. Sim mulation is also of great intterest for designing the sensor to be used, opptimizing its size s and shapee, or for adaptiing existing equipment to speccific needs”.

Figu ure 2.23. Ultra asonic inspecttion of a welde ed part (source: 123rf.com/Jara 1 awa Janterb)

COMMENT ON FIGUR RE 2.23.– Ultrrasonic inspec ction is a non-destructive innspection methodd for detectingg defects withhin a materiall, such as in a welded areaa. Several techniqques can be used. u “Single--element” ultrrasonic NDT T uses a sensoor/emitter that annalyzes the ref eflection of the wave in thee material – as a shown in tthe figure above. As an indu dustrial adapttation of meedical ultrasoound, “multi--element” ultrasoound NDTs usse several inddependent sen nsors/receptorrs, which improves the sensitivvity and resollution of the analyzed a signa al. Another teechnique, TOF FD (Time Of Fligght Diffraction), is based on o the exploita ation of diffraacted signals. Not very sensitivve to the typee, location, geeometry and orientation o off anomalies, thhe TOFD allows,, in many casees, efficient deefect detection n.

Figure 2.24. Simullation of the co ontrol of a sha aft by multielem ment ultrasou und (left) and comparison with w the experim ment (right) [D DUP 14]. For a color version n of this figure, see www w.iste.co.uk/sig grist/simulation n2.zip

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COMMENT ON FIGURE 2.24.– Developed by the List Institute at CEA, the CIVA code is a tool for the numerical simulation of non-destructive ultrasonic testing. It allows us to size a control element, to adjust its parameters in order to obtain a beam focusing or diffusing the energy on the part to be inspected. Simulation assists engineers in preparing for the control. The calculation makes it possible to study the interaction of the beam with the geometry of the part and to simulate the signal obtained in the presence of anomalies. The calculation tool integrates the modeling of many defects, both surface (such as flat or multifaceted cracks) and volumetric (such as holes). While the reality of industrial projects and products sometimes brings surprises or difficulties that the digital tool cannot predict, simulation offers the possibility of anticipating the controllability of parts and can, in some cases, lead engineers to review the design in order to make them controllable. In a few years, simulation has changed the practice of NDTs and has gradually developed as a tool to complement the skills of experts in this field: “The overall approach, simulation and implementation of controls, is based above all on the expertise of the controllers; the results are interpreted in the light of our experience with NDTs. Simulation is also a communication and training tool for our customers and partners. It has thus become an integral part of our service catalog and contributes to offering them at the best price”. 2.3.3. Producing in the digital age 2.3.3.1. Factory of the future The Brazilian photographer Sebastião Salgado [WEN 14] published at the end of the 1990s a book entitled La main de l’homme (meaning ‘the hand of man’), in which one can feel the gaze of the economist, his youth training. It is a look driven by the need to carry out an inventory of the work places in the world. At a time when the digital economy was emerging, with the Internet for the general public in its infancy, he had the intuition that work, especially manual work, was not disappearing, and he told it in its diversity [SAL 98]: net and boat fishing in the Mediterranean Sea, tunnel construction under the Channel, cultivation and harvesting of sugar cane and coffee in tropical areas, ship dismantling in India, textile manufacturing in sweat shops in Asia, fire-fighting on oil wells in Iraq. Humans and their bodies, very often mistreated by exhausting work, from which they derive their livelihoods, suffering as well as dignity. Some of his photographs, showing the work of workers in factories or on construction sites, testify to some of the most trying conditions faced by humans, which, in the Western world, are sometimes entrusted to machines. The human hand is imitated by robots performing various tasks that are increasingly complex, fast and precise.

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In the industrial sector, robots perform repetitive tasks, their use being adapted to the productivity and quality requirements of mass production. However, human know-how remains a guarantee of quality: delicate operations requiring precise execution are, in many cases, carried out by manual labor. Some of the engineers’ research concerning the factory of tomorrow [KOR 16, TAT 18] aims to relieve humans in the performance of delicate and difficult tasks when they are carried out over time. A part of the robotic developments concerns collaborative robots, capable of adapting to human gestures by anticipating and accompanying them (Figure 2.25).

Figure 2.25. Collaborative robot (source: © RB3D/www.rb3d.com)

Jean-Noël Patillon, scientific advisor of the List research institute at the CEA (one of France’s pioneering centers in this field), explains what cobots are: “For many tasks performed with tools, human know-how is irreplaceable. ‘Cobotic’ researches aim to develop systems that adapt to humans. They make it possible to build systems capable of learning in real time about human actions. Like models made in biomechanics, cobotic engineers develop ‘digital twins’. An abstract representation as close as possible to the human being. The models specific to each operator are coupled with automatic learning techniques operating in real time and making it possible for the human and robot to collaborate”. The digital twin, the numerical modeling of a physical process, is no longer reserved for mechanical systems: body modeling also serves humans. It makes it possible to support them and, as we will see in the case of biomechanics, to heal them (Chapter 6). Virtual and augmented reality also complete the range of digital techniques shaping the factory of the future: – virtual reality refers to a set of techniques and systems that give humans the feeling of entering a universe (Figure 2.26). Virtual reality gives us the possibility to

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perform in real time a certain number of actions defined by one or more computer programs and to experience a certain number of sensations (auditory, visual or haptic, for example);

Figure 2.26. Ergonomics demonstration using virtual reality at the French institute List in CEA (source: © P. Stroppa/CEA)

– augmented reality refers to a virtual interface, in two or three dimensions, enriching reality by superimposing additional information on it. Virtual or augmented reality also allows manufacturers to simulate operating conditions or machine assembly conditions. These digital techniques make it possible, for example, to train operators in delicate operations and to carry them out with increased safety and ergonomics. 2.3.3.2. Additive manufacturing Additive manufacturing, which began at the end of the last century, is nowadays undergoing increasing development. Many processes are developed to produce a wide variety of objects [GAR 15]. They are of interest to many industrial sectors, including mechanical engineering (production of spare parts) or the medical sector (production of prostheses and orthoses), etc. Initially used for rapid prototyping purposes, additive manufacturing nowadays makes it possible to produce parts with complex shapes in a short time. It changes the way certain equipment is designed and produced, explain Loïc Debeugny [DEB 18] and Raphaël Salapete [SAL 18], engineers at ArianeGroup: “Some components of the ‘Vulcan’ engine, which powers the Ariane V rocket, are produced using the ‘laser powder bed fusion’ process. Aggregating metal powders with a small diameter laser, this process makes it possible to produce, layer by layer, parts of various shapes with remarkable properties (mechanical resistance, surface finish, etc.). Additive manufacturing makes it possible to design ‘integrated’ systems

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and thus contributes to shortening procurement times or reducing the number of assembly operations. It supports, for example, the strategy of reducing production costs for the future ‘Prometheus’ engine. Designed to develop a similar thrust, the two engines provide the main propulsion for Ariane rockets. The objective for ‘Prometheus’ is to reduce the production cost of each engine from 10 to 1 million euros!” Numerical modeling supports the optimization of additive manufacturing processes, whose technical advances remain even faster than those of the calculation tools used to simulate them. Simulation meets two main needs: to optimize the operating parameters of the additive manufacturing processes used for the mass production of generic parts and to anticipate the difficulties of manufacturing new or specific parts. The calculation makes it possible, on the one hand, to adjust the parameters of a known process in order to obtain a part with the best mechanical properties and, on the other hand, to develop this process for new parts. In the latter case, the simulation makes it possible to anticipate the risks incurred at the time of manufacture: appearance of defects or cracks in the part, the stopping or blocking of manufacture, etc. “We have built our calculation process on the experience acquired with the numerical simulation of welding processes. For this application, the calculations contribute to choosing the welding process, evaluating its influence on the residual deformation of the assemblies or validating and optimizing the welding ranges. They also help to understand certain manufacturing anomalies. For welding or additive manufacturing, a ‘complete’ calculation gives the most accurate information. It requires modeling the thermal and mechanical phenomena involved, in particular the contribution of heat from the source (electron beam, electric arc or laser) and possibly the transformations of matter. Giving access to the distribution of temperature and stresses in the mechanical parts, these simulations generally require significant computation time and have to be carried out by specialized engineers”.

(a) Test specimen

(b) Calculation of temperature (left) and stresses (right) in the specimen

Figure 2.27. Thermomechanical numerical simulation of an additive manufacturing process on a specimen (source: © ArianeGroup). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 2.27.– The figure shows a calculation of the temperature and stress fields in a test specimen obtained by the “laser powder bed fusion” process. The simulation, which accounts for the thermal and mechanical phenomena that develop in the part, uses the so-called “element activation” technique. The numerical model is built from a mesh in which the computational elements are gradually integrated into the simulation, thus solving the equations on a domain updated during the computation, in order to represent the material additions. This type of simulation, operated on a model made up of small meshes, mobilizes a computer for nearly 20 h. It is useful to engineers to calibrate process parameters, including heat source application time, heat flow power and material cooling time. “As part of the development projects for ‘Factory 4.0’ within ArianeGroup, more efficient simulation tools are being deployed in design offices and manufacturing methods. These simulations are based on a mechanical calculation, which is less expensive than a calculation that ‘explicitly’ includes thermal effects. The latter are represented ‘implicitly’ by induced deformations, which are identified by means of test or calibration specimens for a given material and process. This method, known as the ‘inherent deformations’ method, also used in the numerical simulation of welding for large structures, is used as a standard for the development of complex part manufacturing ranges”.

(a) LSPH collector of the “Vinci” engine

(b) Prediction of shape obtained by additive manufacturing with numerical simulation

Figure 2.28. Additive manufacturing of a real part: numerical simulation with the “inherent deformations” method (source: © ArianeGroup). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.28.– Simulation of additive manufacturing processes with the “inherent deformation” method makes a good compromise between accuracy and computation time. Integrating all the physics, it allows us to anticipate the

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deformations undergone by the part during its manufacture with a reliability considered very satisfactory by the engineers. The calculation presented here gives the final state of an engine component for the Ariane VI rocket. It is carried out using a calculation code used by design engineers, to whom research engineers occasionally provide the technical expertise necessary for the implementation or interpretation of the calculation results. This type of numerical approach to additive manufacturing is nowadays implemented by many manufacturers, particularly in the aerospace and maritime construction sector (Airbus, Safran, ArianeGroup, Naval Group, etc.). Contributing to the renewal of industrial production methods, additive manufacturing is becoming one of the essential components of tomorrow’s plant, which is progressing in conjunction with numerical simulation. 2.4. Improving performance 2.4.1. Increasing seaworthiness In 2016, the Modern Express, a cargo ship more than 150 m long, flying the Panamanian flag and carrying nearly 4,000 tons of wood, drifted for several days off the French and Spanish coast. Lying on its side, listing, it was at risk of letting in water, and its fuel polluting the ocean. The ballast tanks, used to improve the stability of the ships, were not operated properly by the cargo ship’s crew: filled on the wrong side of the ship, they increased the ship’s inclination, instead of decreasing it in dangerous sea conditions. Such a situation, attributed to human error, happens only rarely. It is, as far as possible, anticipated at the time of ship design: stability studies, for example, are among the most stringent regulatory requirements in shipbuilding (Figure 2.29). From the comfort of the passengers on board cruise ships to the integrity of the cargo loaded on a merchant ship, to delicate maneuvers such as landing a helicopter on a frigate: sea-keeping is about the operability and safety of all marine platforms. Many calculation methods contribute to this, explains Jean-Jacques Maisonneuve, an expert in the field at Naval Group/Sirehna: “The overall behavior of an offshore platform is first studied by means of ‘wave calculations’: from a three-dimensional model of the ship, engineers calculate the amplitude of its movements (three translations and three rotations) when it receives a wave whose frequency and relative direction in relation to the hull are known. Determined for each vessel by means of specific calculation codes, these ‘transfer functions’ are calculated once and for all. They are then used to evaluate more complex

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sea configurations, combining the amplitudes of motion calculated for the basic directions”. A statistical calculation is used to evaluate the displacements, accelerations or forces experienced by the ship during its overall movement in response to different swells, according to their amplitude, and for different speeds or impacts of the vessel encountering them (Figure 2.30).

Figure 2.29. Stability study of a ship, carried out with the MAAT-Hydro calculation code (source: Marc Chausserie-Laprée/www.mchl.fr)

COMMENT ON FIGURE 2.29.– The stability curve shows how a vessel’s “righting torque” evolves as a function of its heel angle. A positive torque arm means that the combined effect of the hydrostatic thrust and weight of the vessel in the opposite direction tends to return it to its original position when it moves away from it: the boat is stable. The area under the stability curve indicates the mechanical energy required to heel the vessel to a given angle. It is used to assess the ship’s righting ability and it yields useful data for engineers conducting stability studies. “When they were defined by the International Maritime Organization (IMO) in the late

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1980s, the general opinion was that regulatory stability criteria should be developed in the light of the statistical analysis of the stability parameters of ships involved in accidents and of ships operating safely. Conducted by the IMO in 1966 and 1985, this vast survey made it possible to prescribe the stability criteria that its member countries can apply in their national regulations”, explains Marc ChausserieLaprée, a naval engineer and expert on these issues. “These criteria were initially developed for cargo, passenger and fishing vessels. They were then extended to other types of ‘ships’: drilling platforms, dredging equipment, submarines, yachts, etc.”. Stability calculations are performed assuming the vessel is stationary and navigates in calm water. A stability curve is calculated with the shape of the hull and the load cases as input data. These consist of the characteristics of the vessel in the light state calculated from the “mass estimate” (mass distribution of bulkheads, decks, materials, equipment, etc.), to which are added various loading conditions according to the type of vessel: passengers, containers, fish, etc. The “consumable” products such as fuel and water are then added: they vary during navigation and therefore require the calculation of different loading cases. The “free surface” effect, intrinsically variable, should also be taken into account: in partially filled tanks, the movement of fluids changes the position of the ship’s center of gravity and may thus reduce its stability. The damage stability calculations of one or more compartments are much more complex. “The so-called ‘probabilistic’ stability requires, for example, calculating several thousand stability curves by combining several hundred damage cases for different loading conditions. The software calculates the probability that certain compartment assemblies will be flooded simultaneously and the probability that the vessel will ‘survive’ this damage. Several hours of calculation are then required to be compared with the stability analysis for an intact ship, which is obtained almost instantaneously”. The data thus produced are compared with operability criteria, making it possible to demonstrate the ship’s operational safety under the most probable sea conditions. “Wave response calculation methods give indications of the ship’s behavior at sea... but cannot account for certain situations encountered more rarely in difficult sea conditions. Waves breaking on a ship’s deck, the impacts of the bow on waves, etc. Engineers study these configurations using numerical simulations based on the ‘complete’ equations of fluid mechanics”. In some cases, the models aim to represent both the ship’s movements and the hydrodynamics of the flow. Representing this “fluid/structure interaction” (Box 2.2) is necessary, for example, to study a ship stabilization system using controllable fins (Figures 2.31 and 2.32). Allowing the system and its operation to be accurately represented, simulations are carried out in an effort to improve current solutions.

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(a) Wave spectrum

(b) Pitch movement of the vessel Figure 2.30. Analysis of sea-keeping (source: Sirehna/Naval Group). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.30.– The sea-keeping analysis is based on data describing the hydrodynamic loading and on a numerical model of the vessel. The wave spectrum (a) represents the amplitude of waves according to their frequency in all directions; the calculation makes it possible to evaluate the amplitude of the ship’s movements at different incidences (b) according to the wave period.

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(a) Stern and fins

(b) Front and bottom view Figure 2.31. Numerical model of a ship with stabilizer fins [YVI 14]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Figure 2.32. Simulation of wave resistance [YVI 14]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 2.32.– The figure shows the calculation of the vessel’s rolling condition with passive (left) and active (right) stabilizing fins for two moments of oscillation. The simulation is used to represent the increase in the free surface level and the value of the pressure coefficient in both cases. It highlights the contribution of the active stabilization device. 2.4.2. Limiting noise pollution Published in 1837, Les voix intérieures is a collection of poems by Victor Hugo (1802-1885), in which the writer seems to celebrate these times of introspection, which flourish ideally in periods of calm. In these moments of meditation, sounds, sometimes giving all their relief to silence, are not as harmonious or soft to our ears as those from a distant sea, which one hears without seeing: What’s this rough sound? Hark, hark at the waves, this voice profound that endlessly grieves nor ceases to scold and yet shall be drowned by one louder, at last: The sea-trumpets wield their trumpet-blast. (Une nuit qu’on entendait la mer sans la voir, [HUG 69], translation by Timothy Adès4. The transport industry in general, and the air and maritime transport industries in particular, is one of the most involved in the search for technical solutions to reduce noise pollution. The control of acoustic signatures of maritime platforms is therefore a major challenge for manufacturers in the naval sector5: – for manufacturers of passenger ships, being able to justify a comfort brand is a factor that sets them apart from the competition. It thus meets an increased demand from ship owners: the noise and vibration criteria, defined in terms of permissible noise levels in cabins, for example, are becoming more and more stringent in the ship’s specifications;

4 http://www.timothyades.co.uk/victor-hugo-une-nuit-qu-on-entendait-la-mer-sans-la-voir. 5 It should be noted that the study of noise and vibration is not only aimed at the acoustic comfort of human beings: the impact of noise pollution on underwater fauna (cetaceans, cephalopods, etc.) is scientifically highlighted and is receiving increasing attention.

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– forr military navval shipbuilderrs, controlling g the ship’s acoustic signatture is an essentiall element in order o to guaraantee its steallth in many operational o coonditions. The connstraints of suubmarine steallthiness, for example, e popuularized by thhe fiction The Hunnt for Red Octoober [CLA 844, TIE 90], aree among the sttrongest in theeir design [BOV 16, REN 15]. Numerical simulation s is a tool that iss increasinglyy used in s to demoonstrate and juustify the expected vibratioon performancce (Figure various stages 2.33).

Figure 2.33. Numeriical simulation n of ship vibrattions: example e of acoustic rradiation from a subm marine [ANT 12]. For a colorr version of thiis figure, see o.uk/sigrist/sim mulation2.zip www.iste.co

COMMEN NT ON FIGURE E 2.33.– The numerical n mod dels used by shipbuilding s eengineers strive too reflect the dynamic behavior of the ship to scalee. They incluude many structuraal details, succh as decks, bulkheads, su uperstructuress, engines, annd so on, and a modeling m of different d mateerials perform ming differentt functions (sstructural resistancce, soundprooofing, fireproofing – and, in some casses, even decooration!). Dependiing on practicce, models mayy include finitte elements off different typees (shells, beams, volume v or poiint elements, connecting ellements, etc.) in order to aaccurately represennt the ship. Thhe number of equations e to be b solved in thhis model thuss becomes significaant, containingg several hunndred thousan nd, even a feew million, deegrees of freedom,, and the calcuulations requiire appropriatte computer reesources. The propulsive chain, c consisting of the engines, trannsmission annd power e is the maain source conversiion componennts (shaft line, speed reducer, propeller, etc.), of noise on a ship [BO OV 16]. This spreads throu ugh the inner structures andd the hull t limit it, for example by using u dampingg devices into the ocean and designers seek to 2 (Figure 2.34).

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Figure 2.34. Numerical model of a suspension mount [PET 12]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.34.– Made of elastomeric materials, suspension mounts are used in many land, sea and air vehicles. They are designed to isolate a machine or equipment, thereby helping to limit the noise emitted by the former and reduce the vulnerability of the latter to shock and vibration. Numerical modeling helps to optimize, for example, their damping performance. Simulations require a detailed representation of the mechanical behavior of elastomeric materials in a wide range of operating ranges. Turbulent flows are also a source of vibratory excitation of many structures [PAI 04, PAI 11]. These phenomena occur in various situations, for example: – aerodynamic or hydrodynamic lifting profiles (aircraft wings, ship rudders or propellers, etc.) or bluffed bodies (solar panels, tiles, cables, towers, chimneys, etc.); – energy generation and recovery devices (tube bundles, wind turbines, hydroturbines, fluid networks, etc.). These vibrations are associated with undesirable effects: – premature wear and tear, which can jeopardize the safety of installations; – significant noise emissions, a source of noise pollution impacting ecosystems, or discomfort for passengers on means of transport. Turbulent flows (Figure 2.35) also generate vibrations among the structural elements of ships (hull, deck, etc.): these are among the many possible causes of submarines’ acoustic indiscretions.

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Figure 2.35. Developmen nt of a turbulen nt boundary la ayer on a wall

COMMEN NT ON FIGURE E 2.35.– When n the fluid flow on a wall becomes b turbuulent, the wall presssure fluctuattes significanttly. The variou us turbulent sttructures deveeloping in the flow carry an eneergy, more or less significant according to their size, sufficient T physics of the turbulen nt boundary layer, l and its different to causee vibrations. The regimes, is well charracterized by researchers in fluid mechhanics who bbase their dge on numeroous experimental studies [SC CH 79]. knowledg Enginneers have a lot of emppirical data on o turbulent excitation. T These are represennted by turbuleence spectra representing th he intensity off the turbulentt pressure field over a given frrequency rangge (see Figurre 2.36). Thee figure highllights the variabilitty of the expeerimental data: this is one off the difficultiies faced by enngineers.

Figure 2.36. 2 Empirica al spectra of tu urbulent excita ation [BER 14]]. For a color vversion of this fig gure, see www w.iste.co.uk/siigrist/simulatio on2.zip

COMMEN NT ON FIGURE E 2.36.– The fig gure shows seeveral models of turbulent eexcitation spectra, obtained byy different fluuid mechaniccs researcherrs for “simpple” flow G 04, SMO O 91, SMO 066]. The spectrrum gives configurrations [CHA 80, EFI 82, GOO

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the evolution of the pressure according to its frequency of fluctuation. The quantities are represented in the conventional form, known to experts in the field. The data are obtained in “ideal” configurations, which are often far from real applications. Despite their limitations in validity, in some cases they are the only information available to engineers to analyze turbulence-induced vibrations. Which model is the most suitable for calculations? What are the variations in the simulation results? To what extent are they attributable to the input data? Numerical simulation helps to answer such questions and reduce the degree of empiricism that remains in some flow-induced vibration calculations, as explained by Cédric Leblond, an expert in the field at Naval Group: “We use numerical simulation of turbulent flows with RANS methods to feed a theoretical model which calculates turbulent excitation spectra in more general configurations than those delimiting the current validity of empirical spectra. Calculations are used to extract data characterizing the physics of the turbulent boundary layer. The models we develop use this information to calculate the fields contained in the equations describing the evolution of the pressure field”. With this so-called “hybrid approach” [SLA 18], engineers take advantage of the accuracy of numerical calculations and combine it with the ease of use of turbulent excitation spectra. Validated on simple configurations (Figure 2.37), the method allows them to calculate excitation spectra for configurations representative of actual ship navigation conditions.

Figure 2.37. Numerically calculated and empirically determined turbulent excitation spectrum [SLA 17]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 2.37.– The figure shows the turbulent excitation spectra corresponding to two simple water flow configurations – on a flat wall, at two different speeds. The quantities are represented in the conventional form, known to experts in the field. Spectra calculated with a numerical method are represented as green lines, and spectra determined with an empirical model as black lines. The figure shows that the two types of spectra are very close, which validates the numerical calculation method. The latter can be used by engineers to calculate excitation spectra for real configurations, while empirical spectra may only be valid in particular situations. More accurate turbulent flow calculations allow for a direct characterization of turbulent excitation. Simulations are very expensive when they represent increasingly fine-grained turbulence scales, so researchers are constantly improving numerical methods. One of the challenges in aeronautical and ship-building is to calculate flows around large objects, with a resolution fine enough to capture the details of vortex dynamics. Solving the Navier–Stokes equation requires very fine mesh sizes, especially near a wall. In some flow configurations, the size of the models to be implemented in a calculation becomes an obstacle to the implementation of simulations for industrial applications. Simulations based on other models than the one contained in the Navier–Stokes equations make it possible to reduce the cost of calculation while maintaining such fine mesh sizes. The Lattice Boltzmann Method (LBM*) is one of them. Widely used for compressible flow simulations such as those encountered in aeronautics and the automotive industry, it has developed in these sectors over the past decade. Aloïs Sengissen, expert engineer of this method at Airbus, comments: “Flow simulations based on an average description of Navier-Stokes equations (the RANS models), allows for calculation at computational costs that are compatible with project deadlines. They give good results when we try to evaluate the aerodynamic characteristics of aircraft, for instance. Providing average quantities (pressure, speed), they are unsuitable for aero-acoustic problems, studied, for example, for the prediction of noises which by nature are unsteady phenomena. Finer methods, such as simulating the main turbulence scales from the NavierStokes equation (LES modeling), are too time-consuming to model and calculate. The LBM method, the development of which has benefited from innovations in HPC calculation, offers us the possibility of finely

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simulating flows, at modeling and calculation times acceptable for many industrial applications”. This method is based on the Boltzmann6 equation, which describes flows at a scale different from that underlying the Navier–Stokes model. By taking a step back, it is possible to categorize flow modeling according to three scales typically used by fluid physicists: – representing the interactions between fluid particles, such as gases, the “microscopic” description requires solving a large number of degrees of freedom. It is a question of describing, according to the principle of action/reaction explained by Newton’s third law, the force exerted by each particle on the others. This approach is out of reach for dense flows; – at the opposite end, translating the principles of conservation of mass, momentum and energy, the Navier–Stokes equations describe flow on a “macroscopic” scale; – Boltzmann’s equation models the flow at the “mesoscopic” scale, intermediate between the two previous ones. Taking as unknown mathematical functions that account for the statistical distribution of particles in a flow, Boltzmann’s model describes their kinetics using a transport equation, accounting for collisions and particle propagation. The flow quantities, useful to engineers (such as pressure and energy), are deduced from the distribution functions thus calculated. Solving the Boltzmann equation does not necessarily require a structured mesh coinciding with a wall, as required by the finite volume method (Figure 2.38). This contributes to the effectiveness of the LBM method, comments Jean-François Boussuge, a researcher at CERFACS*: “Algorithms developed in the LBM report on the propagation of particles and the collisions they undergo. These are calculated for points constituting a network, which can be refined more immediately than the calculation mesh deployed for solving the Navier-Stokes equations. The network can thus be precisely adapted to complex geometries, taking into account the structural details of aircraft, automobiles, etc., which must be represented for acoustic studies. It is these singularities that are responsible for the pressure fluctuations causing vibrations and noise generated by the flow”.

6 Established by the Austrian physicist Ludwig Eduard Boltzmann (1844–1906), who helped to develop a mathematical formalism adapted to the statistical description of fluids.

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Figurre 2.38. The calculation c grid d used in the Lattice L Boltzm mann Method ccan be adap pted to comple ex geometries s (source: © Aiirbus)

In response to the need of desiggners to have simulation off unsteady pheenomena, particulaarly necessaryy to estimate flow f noise, th he LBM is noowadays used by many engineerrs in the aeronnautics and auutomotive indu ustry (Figure 2.39). Aloïs S Sengissen testifies: “Frrom acousticss to aerodynaamics to therrmics, we aree now simulaating manny fluid dynaamics problem ms using the Lattice L Boltzm mann Method. The sim mulation is useed to address some s unsteady y flight configgurations, succh as the near stall flight f regime,, where a loss of lift is feared. LBM M is parrticularly effeective using ‘massively ‘ paarallel’ algoriithms and alllows calcculations to be b carried ouut in these sittuations, whicch would nott be acccessible to us with w any otherr numerical methods”. m

Figurre 2.39. Flow simulation s on an aircraft usiing the Lattice e-Boltzmann m method (source e: ©Airbus). Fo or a color vers sion of this figu ure, see www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 2.39.– The figure f shows a numerical simulation s off a weakly compresssible turbuleent flow arouund an Airbus aircraft. The objectivve of the calculatiion is to captture as accurrately as posssible the wakke dynamics ggenerated

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downstream of the nose landing gear. Impacting rear axle doors, the intensity of the vibrations generated by vortices particularly affects gear noise or mechanical wear. The calculations thus help to predict their life expectancy. Such a simulation uses a numerical model of significant size. Several hundred and even thousands of processors operate in parallel on a supercomputer in order to realize it [SEN 15]. 2.4.3. Protecting from corrosion Corrosion is an alteration of a material by chemical reaction and is feared by plant designers and operators in many economic sectors, particularly marine platforms. By taking into account all means of combating corrosion, replacing corroded parts or structures, as well as the direct and indirect consequences of the accidents it causes, corrosion induces costs that are estimated at nearly 2% of the world’s gross product and consume, for example, nearly 300 million tons of steel each year [NAC 02]. Corrosion affects, to varying degrees, all kinds of materials (metallic, ceramic, composite, elastomeric, etc.) in varying environments. The corrosion of metals results, in the vast majority of cases, from an electrochemical reaction involving a manufactured part and its environment as reagents. A “multi-physical” problem par excellence, corrosion can be approached by numerical simulation, explains Bertil Nistad, modeling expert at COMSOL: “The finest simulations are based on a set of equations that capture in as much detail as possible the electrical, chemical and mechanical phenomena involved in corrosion. The models describe the environment and electrical state of the part studied, in terms of concentration of charged species, oxygen levels, surface treatments and protections, or presence of marine deposits, etc. and are generally supplemented by experimental data. The finite element method is one of the most widely used in simulations: it solves model equations – the most elaborate of which are based on nearly ten non-linear and coupled equations”. Calculations allow us to, for example, understand the physics of the phenomena involved [KOL 14, WAT 91], as illustrated in Figure 2.40. They can help to evaluate the effectiveness of a protection system, such as cathodic protection. The latter reduces the corrosion rate of a metallic material in the presence of an aqueous medium. By circulating an electrical current between an auxiliary electrode and the material to be protected, the latter is placed at such an electrical potential that the corrosion rate becomes acceptable over the entire metal surface in contact with the aqueous medium. The simulation optimizes the placement of the electrodes to ensure optimal protection (Figure 2.41).

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Figure 2.40. Simulation helps to understand the evolution of corrosion. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 2.40.– The figure is an example of a simulation of the development of point corrosion: the numerical method is used to represent and evaluate the propagation of the corroded material front [QAS 18].

Figure 2.41. Modeling of a corrosion protection system for a ship’s hull (source: image produced with the COMSOL Multiphysics® code and provided by COMSOL/ www.comsol.fr). For a color version of this figure, see www.iste.co.uk/sigrist/ simulation2.zip

COMMENT ON FIGURE 2.41.– The figure shows the electrical current map calculated around a ship’s hull equipped with a protective electrode. By identifying areas likely to present favorable conditions for the development of corrosion, the simulation helps to optimize the design of the protection device. This type of simulation also makes it possible to dimension it by limiting its electrical signature, an important issue to ensure the discretion of certain military vessels, such as submarines [HAN 12].

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Beyond this example of application to the naval field, corrosion simulation is of interest to many industrial sectors, such as offshore construction, nuclear energy, rail transport and steel construction as a whole. 2.4.4. Reducing energy consumption The shape of car bodies has been constantly refined to achieve remarkable aerodynamic performance today, helping to reduce fuel consumption. Shipbuilders also proceed in the same way, seeking the most efficient forms of hulls to satisfy sometimes demanding sailing criteria – in particular in terms of seaworthiness, an environment that is in some respects more restrictive than land. Pol Muller, hydrodynamics expert at Sirehna/Naval Group, explains how numerical simulation fits into a loop for optimizing hull shapes: “We have developed a digital strategy that helps to design ‘optimal’ hull shapes for different design constraints and performance objectives. The first are, for example, the stability of the ship, its transport capacity, when one of the second is, for example, the reduction of the resistance to forward motion, which directly influences energy consumption”. This optimization approach is known as “multicriteria” because it aims to take into account all design parameters in the analysis that takes place in several stages. Carried out for the first time on a small trawler, it is generic and now applies operationally to all types of vessels. “Starting from a hull shape established according to state-of-the-art techniques, we first explore different possible shapes, varying the dimensions using a ‘parametric modeler’. Carrying out the operation automatically, this tool makes it possible to create a set of different shapes according to ‘realistic’ architectural choices: length and width of the ship, angle of entry of water from the bow, etc. In a second step, we determine by means of more or less complex calculations the different performance criteria of these virtual vessels. Stability is assessed by means of graphs, when the resistance to forward motion requires fluid dynamics simulations, for example”. The entire process is automated and preliminary tests guarantee the robustness of the developed calculation chain. It can be used as a decision support tool, with engineers analyzing certain calculations in order to understand the influence of a design parameter on the ship’s performance, or as an optimization tool (Figure 2.42), with the algorithm selecting parameters that can satisfy the constraints of the

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calculatiion (e.g. stability requirem ments) and wo ork toward thhe objectives set (e.g. minimiziing resistancee to forward motion). m Afterr some modiifications by naval architeects, the shappe determined by the algorithm m is then maanufactured. A sea testing campaign wiith both typess of hulls validatess the simulatioon models, onn the one han nd, and the peerformance prredictions given byy the calculatioon, on the other hand (Figurre 2.43).

Figure 2.42. 2 Optimiza ation of hull sh hape (source: © Sirehna/Navval Group). Fo or a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 2.42.– The figure f represeents the initiaal shape of a trawler’s hull, whhich is then modified m by thhe optimizatio on algorithm to achieve loower fuel consumpption, while meeting m the vesssel’s operatio onal requirem ments. In the pprocess, a fluid dynamics calcuulation is perrformed to evaluate e the vessel’s resisstance to forward motion.

Figurre 2.43. Comp parison of hull performance for different ship speeds (source: Sirehna/N Naval Group). For a color ve ersion of this figure, f see www.iste.co o.uk/sigrist/sim mulation2.zip

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COMMENT ON FIGURE 2.43.– The figure shows the evolution of the ship’s power as a function of its navigation speed (the data are presented in a dimensionless form). The comparison of sea trial data with the calculation results highlights the reliability of the simulation process. The comparison of the two hull shapes, initial and final design, shows the gains obtained in terms of energy consumption: it is reduced by nearly 40% at the highest speeds. Numerical simulation changes the practices of engineers in the industry and also gives them the opportunity to develop them. To this end, practitioners must also rethink their relationship to the tool they use – this is reflected in Pol Muller, who is left to conclude this chapter: “Because it is not constrained by any ‘preconceived notion’ or ‘empirical reflex’, the algorithm can sometimes be more ‘creative’ than a naval engineer! Exploring forms that intuition can initially reject, the algorithm can thus allow architects to become aware that bold choices, offering unexpected performances, are possible... and above all feasible!” Fluid/structure interaction refers to the exchange of mechanical energy between a fluid flow and a deformable solid in which develops on contact. The loading of fluid on to structures exposed to their action and, more generally, the detailed knowledge of the mechanical coupling mechanisms between a flow and a vibration is a problem shared by many engineers in different sectors [AXI 07, PAI 04]. It is potentially found in many situations in aeronautical and maritime engineering. Other fields are concerned, such as civil or nuclear engineering, automotive or space design – even biomechanics (Chapter 6). Research on fluid/structure interaction was particularly stimulated following the Tacoma Bridge disaster in the United States on November 7, 1940. The structure began to oscillate and twist in response to the moderate wind, which swept it away until it was destroyed in a few hours [WAS 07]. The story of this, thankfully victimless, disaster, whose causes have been debated at length by engineers and researchers, is often told to mechanical engineering students today. The explanation that is now accepted is that of the coupling mechanisms between the torsional movements of the bridge and the formation of eddies in the air in the vicinity of the bridge. Scientists speak of “aero-elastic instability”. A continuous transfer of energy is achieved from the wind to the bridge. Above a certain wind speed, the bridge no longer absorbs this energy. It amplifies its movement until it is no longer mechanically sustainable. When the stresses it supports are too great for the material it is made of, it gives way and breaks. The phenomenon of aero-elastic instability was not known to engineers at the time of the bridge design: they designed the structure with the know-how and practices of their time. Today, bridge design incorporates Tacoma’s lessons [PAI 11]. For instance, the viaduct spanning the Tarn valley in Millau, France (Figure 2.44) has a very aerodynamic shape designed for a particularly windy environment.

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Representing fluid/structure interaction as accurately as possible is a mathematical and numerical challenge that has motivated the development of many calculation methods, some of which have nowadays achieved remarkable reliability [SIG 15]. Take the example of marine propellers: traditionally forged from a copper–aluminum alloy, their manufacture has been shaken up by new processes and materials, such as 3D printing or composites. Lighter, more flexible composite propellers offer good qualities in order to reduce the fuel consumption of certain ships. They have other properties, relevant to civil or military construction [BLA 11, BLA 16]. Composite materials can be used industrially to obtain various blade shapes, whose hydrodynamic efficiency is being optimized.

Figure 2.44. The Millau Viaduct, designed by the English architect Norman Foster and the French engineer Michel Virlogeux, was built by the French company Eiffage between 2001 and 2004 (source: ©Michel Sigrist)

Numerical simulation can help predict the performance of a composite propeller [MOT 11]. The calculations take into account the fluid/structure interaction involved in the operation of the flexible propeller. The pressure and viscosity forces are exerted on the propeller blades and all the elements that compose it, at the same time as its rotation modifies the flow velocity at the blades [YOU 08]. This continuous transfer of energy is represented by two equations, expressing Newton’s third law (Chapter 1 of Volume 1): – The first allows us to calculate the stresses on the propeller blades: (v)n = − n +

(v)n

It reflects the action of the fluid: the pressure force is represented by the first term, and viscosity by the second term;

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– the second is used to calculate the velocity of the fluid near the blades. Translating the reaction of the fluid to the movement of the structure that imposes a speed on it, it is written as: = The challenge of the simulation is to represent this interaction as accurately as possible, as it is one of the keys to the accuracy of the calculation. Researchers and engineers have developed algorithms with the adequate mathematical properties to model fluid/structure interaction. In some cases, the fluid/structure interaction is characterized by the movements induced by the vibration of the structure or by the flow of the fluid. Their modeling can be accomplished in different ways. Discovering the Navier–Stokes equations (Box 2.1), we took a break along a riverside to understand them. Now let us take a seat in a small motorboat and jump into the water. Without a motor, we drift with the current: we follow its movement and the mathematical description we would make of it is called Lagrangian. Let us control the speed of our engine to exactly compensate for the speed of the river: we remain motionless and this time observe the movement around us. This is an Eulerian description: the one that allows a balance to be made on a quantity, for example. The Lagrangian and Eulerian descriptions bear the names of two mathematicians, the French Joseph Louis Lagrange (1736–1813) and Swiss Leonhard Euler, to whom we owe major contributions in mathematics and mechanics, some of which are briefly mentioned in this book. A Lagrangian mesh adapts to movement and can sometimes be so deformed that it is no longer possible to calculate. An Eulerian mesh is fixed: it has a limited ability to describe a sometimes very complex movement. Between the two approaches, the Arbitrary Lagrangian-Eulerian (ALE) mesh takes advantage of the advantages of both descriptions, limiting their disadvantages [SOU 13]. The mesh thus has its own dynamics and adapts to movement (Figure 2.45): it gives potentially more precise results where either the Lagrangian or Eulerian models meet the limits mentioned above.

Figure 2.45. The simulation of the swimming of a fish uses an arbitrary Lagrangian-Eulerian method (source: Alban Leroyer, École Centrale de Nantes)

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COMMENT ON FIGURE 2.45.– “Take your lessons from nature, that’s where our future lies”: these words, attributed to Leonardo Da Vinci, can become the motto of scientists interested in bio-mimicry while proposing solutions inspired by living inventions. The computational algorithms used to simulate a deformable propeller, for example, are based in part on numerical research motivated by an understanding of the hydrodynamics of swimming, such as that of a fish [LER 04]. Lagrangian, Eulerian and arbitrary Lagrangian-Eulerian methods are also widely used to represent the movements of a liquid surface. A situation encountered on many occasions in transport engineering: – In the case of sloshing, describing the movements of a fluid contained in a tank

[SCH 09]. The liquid gas embedded in a rocket or carried by a cargo ship is strongly influenced by the movements of the tank containing it and in turn can affect the launcher’s trajectory or the stability of the ship. For security reasons, it is crucial to understand these phenomena, and numerical simulation makes it possible to account for this coupled dynamic (Figure 2.46).

Figure 2.46. Movement of a fluid in a cryogenic reservoir [KON 19]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip – In the case of slamming, encountered when an object impacts a fluid surface. For example, in shipbuilding, in difficult sea conditions or at high navigational speeds, repeated impacts of a part of the ship such as a bow bulb can damage the structure. During impact, a flow of water is violently projected: simulations accounting for this phenomenon may use ALE methods, with which it is possible to model the overall dynamics of the object and the fluid it ejects (Figure 2.47). In both cases, the calculation methods are compared with experimental test results specifically designed to support the validation of digital tools (Chapter 2 of Volume 1). Let us return to the example of the simulation of the hydrodynamics and mechanical strength of a deformable propeller with representation of fluid/structure interactions. It

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consists of jointly calculating movement and flow. Engineers use a numerical method based on different tools (Figure 2.48): – a hydrodynamic calculation code is used to calculate the pressure on the blades of the turbine; – a mechanical strength calculation code is used to calculate the stresses on the blades and hub; – a third tool, possibly integrated into one or the other of the calculation tools, makes it possible to report on the mechanical coupling between hydrodynamics and mechanical strength. It transfers the necessary information to the two previous codes.

Figure 2.47. Simulation of the impact of an object on a fluid surface [LER 04]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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This calculation strategy, known as “co-simulation”, takes advantage of tools dedicated to physical problems and numerical methods of a different nature. It has become operational after more than 10 years of development, the time necessary to establish the mathematical bases for the digital tools implementing them and to carry out successive validations ensuring their subsequent use. The engineers who implement it thus consider it generally ready for industrial use: – reliable, it provides relevant information for propeller sizing; – precise, it reflects complex physical phenomena that may need to be represented to understand the overall behavior of the propeller; – efficient, it makes it possible to obtain data with computer means that are accessible to them. Coupling Information on the propeller motion (rotation speed, strain)

Hydrodynamics

Mechanics

Calculation of pressure distribution on the blade

Calculation of mechanical stresses in the blade

Coupling Information on the fluid flow (velocity, pressure)

Figure 2.48. Algorithm applicable to the simulation of a deformable propeller. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Calculation times can reach several days, which is acceptable when engineers are looking for complete information, especially in optimization phases. At the end of the project, they have to choose between a very limited number of possible architectures. Simulation makes it possible to compare different designs, for example, on the basis of a criterion defining the performance to be achieved by a blade (e.g. a given state of mechanical stress or expected hydrodynamic efficiency). Box 2.2. Fluid/structure interactions

3 The Universe and the Earth

Contemporary of Newton, Leibniz, and French mathematicians René Descartes (1596–1650) and Pierre de Fermat (1607–1665), Blaise Pascal (Figure 3.1) embodied an ideal form of all of them: that of a knowledgeable man. A physicist, mathematician and philosopher, he evoked, in one of his most famous texts, the singular place of humanity on Earth and in the Universe: “Let humanity therefore contemplate the whole of nature in its high and full majesty, let us keep our sight away from the low objects that surround us. Let us look at this bright light put like an eternal lamp to illuminate the Universe, let the earth appear to us as a point at the cost of the vast tower that this star describes and let us be surprised that this vast tower itself is only a very delicate point towards the one that these stars, which roll in the firmament, embrace” ([PAS 60], translated from French). Are researchers in astrophysics and geophysics, in the 21st Century, the heirs of the 17th Century scientists? With numerical simulation, they nowadays carry out real thought experiments, supported by data, in fields where concrete experimentation is not easily accessible – or even simply possible. Solving certain enigmas of the Universe, which extend Pascal’s philosophical observations, and contributing to the analysis of geophysical risks – in order not to reduce it to a probability calculation – are two areas in which numerical simulation is becoming increasingly important.

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Figure 3.1. Blaise Pascal (1623–1662)

COMMENT ON FIGURE 3.1.– Early inventor of a computing machine (Chapter 4 of the first volume), Blaise Pascal was passionate about physics and mathematics. He was interested in the notion of vacuum, experimented with the laws of fluid hydrostatics and laid the foundations for the calculation of probabilities. His mystical experience turned him from science to theology: his ambition was to write a treatise on it, of which Les Pensées, found after his death, are the working notes (source: Blaise Pascal, anonymous, 17th Century, oil on canvas, Château de Versailles). 3.1. Astrophysics An orchestral explosion punctuated by the percussion of timpani inaugurates the Representation of Chaos. It slowly fades into a long decrescendo ending in a marked silence. In a tiny pianissimo, an uncertain sound world is then born, whose tonality only gradually asserts itself. Through contrasting and apparently erratic episodes, ranging from the imperceptible murmur to the brutal explosion, the overture to The Creation, written by Austrian composer Joseph Haydn (1732–1809), then subsides into a transition giving Raphael the floor. The latter describes, in a short recitative, the world as “formless and empty” of the “dark abyss”. In a pianissimo breath, the choir entered in turn by evoking “the spirit of God” and proclaimed fortissimo “let there be light!” He is accompanied by the entire orchestra, supporting his song to a

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chord of D Major, powerful, radiant and luminous! Uriel concludes with a very short recitative of the introduction to this oratorio: “And God saw that the light was good... God separated the light from the darkness”. First performed in Vienna in 1799, this musical work begins with the first three minutes of the Universe. It seems to anticipate by more than a century the Big Bang theory, an idea supported in the 1930s by the observations of the American astronomer Edwin Hubble (1889–1953). The quest for the origin of the Universe – as well as its possible future – has been built by improving the theoretical knowledge and sensitivity of observational instruments over time. Astrophysicists studying the Universe, its formation and evolution, nowadays have an additional tool at their disposal: computer simulations. Patrick Hennebelle, a researcher at the CEA, at the Institute of Fundamental Laws of the Universe, explains: “For more than twenty years, astrophysics has been taking advantage of numerical simulations. They allow us to understand and predict the behavior of certain celestial bodies and are applied in many fields: star physics, galaxy dynamics, planet formation or the evolution of the gaseous interstellar medium, etc. Simulations make it possible to reproduce astronomical observations, which involve the interaction of systems with highly variable densities, covering a very wide range, typically from 1 to 1010 particles per cm3! The models take into account electromagnetic forces, gravitational force and current research aim to better account for radiation processes, which are still poorly described in some simulations”. Scientific computation also offers researchers the possibility of reproducing evolutionary sequences that cannot be understood in their entirety by other means, because they take place over several billion years! It is also a means of optimizing the use of the most modern astronomical observation resources (Figure 3.2). The latter are shared within an international community and their access, subject to calls for projects examined by expert commissions, is very competitive. Simulation allows researchers to prepare an observation sequence, by testing different hypotheses in advance, and can also be used to interpret the results. Numerical models are becoming widespread in all disciplines of astrophysics, particularly the most advanced ones, contributing to the description of black holes and the search for gravitational waves, whose recent discovery is also due to modeling techniques (Box 3.1).

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Figure 3.2. ALMA is an international astronomical observation tool, a network of 64 antennas installed in Chile (source: © European Southern Observatory/ C. Malin/www.eso.org)

3.1.1. Telling the story of the Universe Our Universe was born some 13 billion years ago and the matter of which it is composed has been sculpted by the action of different fundamental physical forces. While the first few seconds of the Universe are still an enigma to cosmologists, its subsequent evolution is better known. Current physical models explain how the first particles (electrons, protons, neutrons – and beyond, elementary particles they are made of) and atoms (hydrogen and its isotopes, and then the range of known chemical elements) are formed under the influence of nuclear and electromagnetic forces (Figure 3.3). The history of the Universe is therefore that of a long aggregation of its matter that sees the formation of the first stars and galaxies and other celestial bodies (clusters and superclusters of galaxies). This organization is, among other things, the result of gravitational force. The latter is described by Newton’s formula that some astrophysicists use to understand the structure of the Universe. In 2017, for example, researchers conducted one of the most accurate simulations to date of a piece of the Universe, using a so-called “N-body model” [POT 17]. The latter describes the gravitational interaction between a very large number of celestial bodies: the problem posed has no explicit mathematical solution and only a numerical method is able to give one. Romain Teyssier, one of the researchers behind this simulation, explains: “This is a description of the gravitational forces acting on a large set of particles. They are of different sizes, and they represent celestial bodies: stars, star clusters, small or large galaxies (dwarfs or supernova), galaxy clusters, etc.”

Figure 3.3. A summarizing history of the Universe. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 3.3.– This illustration summarizes the history of our Universe, which spans almost 14 billion years. It shows the main events that occurred in the first eras of cosmic life, when its physical properties are almost uniform and marked by very small fluctuations. The “modern history” of the Universe begins some 1 to 10 million years after the Big Bang, from the moment it is dense enough for the gravitational force to orchestrate its global organization. It is marked by a wide variety of celestial structures: stars, planets, galaxies and galaxy clusters. Long considered as the “start” of the history of the Universe, the Big Bang became for modern physicists the marker of a transition between two states of the Universe. The question of the origin of the Universe remains open [KLE 14] (source: ©European Space Agency/C. Carreau/www.esa.int). The simulation figures are, strictly speaking, astronomical. In order to achieve it, scientists use a square digital box, one side of which measures 3 billion parsec1. The calculation box contains 2 trillion particles (2 million million or 2 thousand billion). It allows us to represent galaxies 10 times smaller than our Milky Way, which corresponds, for example, to the star cluster of the Large Magellanic Cloud. The simulation thus involves some 25 billion galaxies, whose evolution is observed over nearly 12.5 billion years and it is carried out in just under 100 h of computation. On the day of the simulation, this resolution is considered very satisfactory by astronomers and astrophysicists. The calculation represents the places where matter has organized itself in the Universe under the influence of gravity (Figure 3.4) and provides data that are sufficiently accurate to be compared with observations made on the cosmos within a few years. Until now, the calculations did not have the accuracy required for this comparison to be relevant. The simulation is made possible through two innovations: – The use of particularly efficient algorithms to model a very large number of particles. Directly simulating the interactions between particles requires operations: for the 2 trillion particles required for simulation, the amount of calculations to be performed is inaccessible to computers, even the most powerful ones! An appropriate method, known as the “fast multipolar method”, considerably reduces the number of calculation operations. It consists of representing the interactions of one particle with others by means of a tree, where the direct approach represents it by means of a network (Figure 3.5). In the tree, the interaction between 1 The parsec is a unit of measurement for long distances, as used in astronomy: 1 parsec corresponds to 3 light years, the distance traveled by light in 3 years, at a speed of 300,000 km/s. It is also the distance that separates the Alpha Sun from the Centaur, the closest star to our galaxy. The size of the simulation domain represents 3 billion times this distance, that is 9 billion light years.

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the partiicles and is representeed by the onee they have with w the particle . By exploring the tree moore or less deeeply, we find all the interacctions described by the ons, while thee network onee requires network.. Exploring thhe tree requires operatio operaations. Under these conditioons, the calcu ulation at 2 trilllion particles becomes possible.. The validattion of the simulation iss obtained byy comparing a direct calculatiion and an opttimized calcullation on a sam mple of a few w million partiicles. The simulatioon describingg the 2 trillionn particles is then perform med with the ooptimized algorithm m.

Figurre 3.4. Simulattion of the statte of the Unive erse organized d under gravittational force es between ce elestial bodies (source: Joac chim Stadel, University U of Zurich)

Figure e 3.5. Interactio ons between particles p can be b described with w a networkk or tree

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– The use of supercomputers that exploit the processing capacity offered by graphics cards (GPUs). Note that 5,000 graphics cards were simultaneously used on the supercomputer of the Swiss National Supercomputing Centre (Chapter 3 of the first volume), whose performance and architecture are currently unique in the world. The 100 hours of computing time required for simulation is entirely appropriate to the pace of the researchers’ work. By comparison, the duration of a parallel calculation on the same number of conventional processors (CPUs) is estimated by researchers at 20 years. So, the calculation code is the result of a development work of about 20 years and its adaptation to the specificities of this simulation took about 3 years. Porting the algorithm to other supercomputers should allow for simulations with 10 or 100 times more particles, thus offering calculations a higher resolution. Legend has it that it was by watching an apple fall to the ground that the British physicist Isaac Newton (1643–1727) began to develop the theory of universal gravitation. It originated from a conversation that Newton’s doctor and confidant, William Stukeley (1687–1765), recounted in his Memoirs of Sir Isaac Newton’s Life (1752): “As the weather got hot, we went into the garden and drank tea under the shade of a few apple trees, just him and me. During the conversation, he told me that he had found himself in the same situation, long before the notion of gravitation had suddenly occurred to him, while he was sitting in a contemplative mood. Why does this apple always fall perpendicular to the ground, he thought to himself. Why doesn’t it fall sideways or upwards, but constantly towards the center of the Earth? And if matter attracts matter in this way, it must be in proportion to its quantity; therefore, the apple attracts the Earth in the same way that the Earth attracts the apple” (quoted by [HER 62]). Whether authentic or invented, the anecdote allows us to conceive Newton’s path of thought. Before the ultimate understanding, presented as sudden, the slow intellectual maturation of a theory has its roots in the observation of the world. For the physicist, it is a matter of expressing it in a general relationship that allows him to give a summarizing account of it, by means of a mathematical writing, the Newton equation being written as:

=−

′

With this equation, Newton states that two bodies attract each other according to a force proportional to the product of their masses (all the greater the greater the size of each one) and unlike the square of the distance that separates them (all the smaller the greater the distance). This force is directed like an arrow u between the two bodies that interact through gravity. G refers to the gravitational constant: it is an invariant quantity, like the number π.

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Apples or planets, stars, galaxies, etc.; all bodies are subject to the effect of gravitational force, which Newton described as universal. In order to conceive his theory, Newton relied on the laws of the German astronomer Johannes Kepler (1571–1630), who studied the heliocentric hypothesis – that the Earth revolves around the Sun, placed at the center of our planetary system – formulated by the polish astronomer and mathematician Nicolaus Copernicus (1473–1543). In his book Mysterium cosmographicum, which he published in 1596, Kepler proposed, among other things, a model of the Universe based on regular polyhedra (Figure 3.6).

Figure 3.6. The Universe model proposed by Kepler is based on five regular polyhedra and is close to the spherical shape symbolizing divine perfection COMMENT ON FIGURE 3.6.– Tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron: Plato’s five solids allow Kepler to construct a model of the Universe by noting that they can be interposed between the orbits of the six planets known at that time [KEP 96, Tabula III: Orbium planetarum dimensiones, et distantias per quinque regularia corpora geometrica exhibens] (source: www.commons.wikimedia.org). The law of orbits, the law of areas and the law of periods describe the main properties of the movement of planets around the Sun. Their orbit is an ellipse, of which one focus is the Sun, the Sun–planet ray sweeps equal areas for equal time intervals and the speed of a planet thus becomes greater as the planet approaches it: it is maximum in the vicinity of the shortest ray (perihelion) and minimal in the vicinity of the largest ray (aphelion). Finally, the square of the period of revolution is proportional to the cube of the half-larger axis of the orbit, according to the relationship / = proposed by Kepler. Newton combined Kepler’s laws with the laws of motion set out in his Philosophiæ Naturalis Principia Mathematica and obtained the form of the equation of gravitation, the driving force behind the motion of the stars.

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It should also be noted that Hypatia (360–415) can be credited, without certainty, with the discovery of the Earth’s elliptical orbit, nearly twelve centuries before Kepler. This is the starting point of Alexandro Amenabar’s film (Figure 3.7) – if not a historical reality.

Figure 3.7. Hypatia is played by Rachel Weisz in the film Agora [AME 09] COMMENT ON FIGURE 3.7.– Hypatia, a Greek philosopher and mathematician, directed the Neoplatonist School of Alexandria in the 4th Century. In Amenabar’s film [AME 09], she is presented as a woman free of spirit, rejecting the social and religious conventions of her time and devoting her life to the search for truth. The movement of celestial bodies was explained by her contemporaries using the Ptolemy system, postulating circular trajectories. The film stages how Hypatia noted the inconsistencies between this description and her observations, and thus discovered that the Earth revolves around the Sun, by describing a circle with two centers, an ellipse. The film also incorporates historical elements, with anachronisms that the experts could discuss at length. It presents the contrasts between reason and superstition, between the power of thought and that of beliefs (source: poster of the film Agora, distributed in France by Mars Films/www.marsfilms.com). With the laws he has laid down, Newton saw the movement of celestial bodies as falling motions. The French writer Paul Valéry (1871–1945) wrote about how Newton imagined movements: “You had to be Newton to see that the Moon is falling when everyone can see that it is not” ([VAL 41], translated from French). Valéry thus explained that Newton’s intuition was to understand and formalize that the falling motion of celestial bodies in the Universe is compensated by the force of attraction that connects them. He also praised Newton’s intelligence, who was able to see our world in a way which was different from common sense.

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On the earth’s surface, we feel the gravity field, which combines the effects of gravitational force and centrifugal force due to the rotation of the Earth – the first being very clearly predominant. The gravity field shows variations due to the uneven distribution of masses on and within the Earth’s surface (Figure 3.8).

Figure 3.8. Geoid: representation of the equipotentials of the gravitational field at the Earth’s surface. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.8.– In 2011, ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite enabled the high-precision measurement of changes in gravity at the Earth’s surface. The geoid, the surface obtained by grouping points of the same gravitational potential, is a reference for many topographic or oceanographic measurements. The accuracy of the data it provides is crucial for the various uses for which it is intended, for example to understand sea level changes, ocean circulation, iceberg drift, land layer dynamics, etc. GOCE is said to have collected an unprecedented amount of data, providing scientists with one of the most accurate geoid data to date (source: ©European Space Agency /www.esa.int). While gravitation fascinates many artists, such as the filmmakers who direct it [CUA 13, VAN 07] or the dancers who experience it [HEY 16, WEN 11], we live with it forgetting its omnipresence, except perhaps in special circumstances. For example, when our buttered bread slice falls to the ground and (almost) always on the wrong side! When it falls from the edge of the table, it tends to slide and turn before being dragged to the ground. The parameters defining the initial state before the fall are the friction of the bread on the table, the height of the table and the size of the toast. The falling distance is not large enough to let gravity prevail over the rotation and friction of the bread on the table as it tilts, so that the toast first undergoes a half-turn rotation before crashing to the

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ground on the buttered side! With a table at least three meters high, the toast can make a full turn and its chances of falling on the buttered side or not are then equivalent to a coin toss: 50–50. But 3-m tables are not part of our daily lives. Humans do not exceed this size: a fall from this height would be fatal to them. Nature does things well by limiting our growth (which it allows for more stable quadrupeds, such as giraffes). Evolving in a world where our tables are necessarily limited in height, our sandwiches (almost) always fall on the wrong side. “We show that toast does indeed have an inherent tendency to land butter-side down for a wide range of conditions. Furthermore, we show that this outcome is ultimately ascribable to the values of fundamental constants. As such, the manifestation of Murphy’s Law appears to be an ineluctable feature of our Universe […]. We end by noting that, according to Einstein, God is subtle, but He is not malicious. That may be so, but His influence on falling toast clearly leaves much to be desired…” [MAT 95]. This is the conclusion of a British scientist, Robert Matthews, with both humor and rigor, who proposes a theoretical and experimental study that helps explain why our breakfasts can sometimes become catastrophic. The theory of universal gravitation, based on a seemingly simple formula, makes it possible to calculate the date of eclipses, the passage of a comet in the sky or an asteroid near our planet. It is also because of Newton’s equation that the French astronomer Urbain Le Verrier (1811–1877) predicted in 1846 the existence and position of Neptune. This was the first time a planet had been discovered through the resolution of mathematical equations. Until then, only astronomical observations allowed it. Having an equation is not enough to predict the orbit of the planets! However, a solution must be found, an explicit mathematical formula that can be calculated. Describing the gravitational interaction between any number of these bodies is a problem that has no analytical solution. The “three-body problem”, describing the interaction between the Earth, Moon and Sun, thus preoccupied, in addition to Newton, Leonhard Euler and Jospeh-Louis Lagrange. In 1772, Lagrange published Essais sur le problème des trois corps (Essay on the three-body problem), in which he calculated the position of points of particular space (Figure 3.9). The attraction forces exerted by two celestial bodies of large mass on a third, whose mass is negligible, compensate each other. This makes it possible to place satellites or observation probes, for example, because the relative positions of the three bodies are fixed. Two of them are “stable” – the objects placed there tend to keep their balance position, like how a marble in the hollow of a gutter remains at rest. The other three are “unstable” – the objects that occupy their position tend to move away from it, like how a marble at the top of a speed bump would roll to a lower point.

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Figu ure 3.9. Lagrange points forr the Sun and Earth. For a color c version o of this ure, see www.iiste.co.uk/sigrrist/simulation2 2.zip figu

COMMEENT ON FIGURE 3.9.– 3 The calcuulation of the po osition of the Lagrange L pointss is done by conssidering the ballance of a bodyy of negligible mass under thee effect of gravvitational forces with w two other bodies, b for exam mple the Earth and the Sun. The T Lagrange L1 and L2 points are a “unstable” ” balances. A neutral n body ca annot remain there t naturally while a probe can c be placed thhere at the costt of reasonable fuel f consumption, as the gravvitational field is weak in its viicinity. The L1 point p of the Ea arth–Sun system m makes it posssible to observee the Sun without interference with the Earth or the Moon, and a thus to deteect solar disturbaances before thhey reach the Earth’s E atmosp phere. It is alsoo the ideal possition for space weather w missionns, such as thee one performeed by SOHO (SSolar and Helioospheric Observaatory) of the Euuropean Space Agency. Locateed nearly 1 milllion and 0.5 killometers from Earth, L2 is the furthest from the Sun. It is close enough to the Earth thhat data collecteed by satellites can be transfeerred to it at a high rate. L2 is i used by majoor space astronoomical observattories launchedd over the pastt two decades, such as the E European Space Agency’s A Planckk satellite (sourrce: © NASA/W WMAP Science Team/www.nas T a.gov). In the t solar system m, the Lagrangee points form a particular set, for f example draawing an optimall trajectory to guide g objects at a a lower enerrgy cost (Figuree 3.10). The A American probe, Genesis, launched in 2001,, was placed in orbit at point L1 and ccollected informaation on the Suun for two yearrs. It was redirrected to point L2, before retuurning to Earth in i 2004 with its precious cargo. c The trajjectory of thiss mission, deffined by researchhers at NASA’s Jet Propulsioon Laboratory, passes near Laagrange points, used as “gravitaational relays”. Unlike a terrrestrial roadway, the shape and directionn of this interplaanetary networkk is constantly changing c with the configuratioon of the planeets in the solar syystem. A trip onn one of the lannes of this “interplanetary highhway” requires minimal energy, but is at the cost of a lonnger travel tim me than that alllowed by a ppropelled trajectoory.

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Figure 3.10. The Interplanetary Transport Network (ITN) passes through the Lagrange points of different planets of the solar system (source: © NASA). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.10.– The figure is an artist’s representation of the interplanetary highway. The green ribbons correspond to one of the possible paths in a mathematically calculated set, represented by the dark-colored tubes. The places where the trajectories suddenly change direction correspond to Lagrange points. A new look is taken at the Universe and gravitation with the work of Albert Einstein [BER 04, LOC 15]. In 1915, he presented the Theory of General Relativity in which he interpreted gravitation not like a force as Newton did, but as the curvature of space time. Einstein’s equations thus establish the relationship between the geometry and curvature of space time (represented by ) and the momentum and energy of a system which evolves in it (represented by ):

=

8

and are matrices (or arrays) that contain 10 unknowns. Solving these equations yields the geometry of space time and the dynamics of systems according to general relativity. For instance, the trajectories of the planets correspond to an inertial movement (in the sense of Newton’s firt law) passing through the shortest path between two points and following the curves of space time, distorted by the presence of very massive celestial bodies, such as the Sun (Figure 3.11). Einstein’s equations can be used to predict the existence of black holes, a topic to which British physicist Stephen Hawking (1942–2018) dedicated most of his life in order to piece together the parts of the puzzle [HAW 88]. One of the densest structures in the Universe, they attract mass, energy and light into the well they dig in space time: no light radiation emanates from it. Black holes fascinate us as much as the scientists who discovered their existence and began to

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understand their properties, which disrupt the conception of time, space, mass and gravitation [NOO 18].

Figure 3.11. Signals sent between the Earth and the Cassini probe (green wave) are delayed by the deformation of space and time due to the mass of the Sun (source: © NASA). For a color version of this figure, see www.iste.co.uk/sigrist/ simulation2.zip

COMMENT ON FIGURE 3.11.– This artist’s representation represents the influence of the deformation of space time by very dense bodies. Here, the path of a signal transmitted from the Earth to a space exploration probe is distorted by the presence of the Sun. The propagation of the signal thus follows the deformation that it imposes on space time. In 1915, Einstein used his theory to explain Mercury’s singular trajectory: the ellipse described by this planet, the closest to the Sun (therefore more sensitive to gravitational effects), rotates slightly faster than it should. Newtonian mechanics does not allow us to fully understand this movement, while Einstein’s calculations explain them well. A second confirmation of the theory of general relativity comes four years later from observations made during solar eclipses. Carried out under the direction of the British astronomer Arthur Stanley Eddington (1882–1944), they highlight the deviation of light rays by the Sun, as shown by Einstein’s calculations. Einstein’s theory further predicts that when two massive objects interact, they produce a “gravitational wave”, a deformation of space time itself, propagating in the Universe at the speed of light, as a wave in a fluid deforms in space and travels over a liquid expanse. If such a wave causes a deformation visible to the naked eye, attested by the movement of

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a floating body, detecting a gravitational wave is not so easy: the deformation it produces is in fact in the order of 10−21 (1 for 1,000,000,000,000,000,000,000). Identifying it is equivalent to measuring the distance from the Earth to the Sun with an accuracy equivalent to the size of the hydrogen atom! Gravitational waves are somehow “hidden” in Einstein’s equations, as waves in a fluid are embedded in the equations of flows. The study of gravitational waves has benefited from researches undergone by mathematicians and theoretical physicists. Early studies in the 1980s involved complex (and tedious!) analytical calculations and, more recently, numerical simulation based on Einstein’s equations have allowed scientists to predict what the signature of gravitational waves would be (Figure 3.12).

Figure 3.12. Simulation of gravitational waves resulting from the interaction between two massive celestial bodies. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.12.– In 2012, a team of NASA astrophysicists was using models to calculate the properties of a gravitational wave and to understand the type of signal it generates. The scientists simulated the fusion of two small black holes using a computer calculation program. The emission of the gravitational wave is visualized in this image which represents the deformations of space time resulting from its passage. The yellow curves near the black holes indicate the regions in which strong interactions occur between the gravitational fields of the two bodies. The simulation is to date one of the most significant among those operated on NASA supercomputers (source: ©NASA/C. Henze). Simulation techniques produce data useful for the development of gravitational wave detection instruments in support of instruments developed by scientists. The result of

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several decades of research, various laser interferometric observatories have been developed worldwide based on international scientific collaborations: Virgo in Europe and the LIGO (Laser Interferometer Gravitational-wave Observatory) in the United States are two examples2.

Figure 3.13. Aerial view of the LIGO interferometer in the United States (Livingstone, Louisiana site)

COMMENT ON FIGURE 3.13.– The interference between two waves is characterized by regions in which vibrations are added or submerged, producing areas of high and low intensity, allowing them to be detected and characterized. This phenomenon is observed in the laboratory for certain electromagnetic waves using an interferometer. The detection of gravitational waves by means of interferometers poses many difficulties: for example, the signals can be disturbed by undesirable vibrations, such as those of seismic waves. Two remote sites in the United States host LIGO interferometers, which allows in particular the comparison of signals, freeing themselves from site effects. Another gravitational wave detector is under construction in Europe (Virgo) and two others, in Japan and India, will complement the observations of the three current detectors. With these tools, whose detection quality is constantly improving, scientists expect to discover the traces of many cosmic events and to understand more precisely the history of the Universe (source: www.ligo.org). The two LIGO detectors, built at the initiative of three American astrophysicists, Kip Thorne, Rainer Weiss and Barry Barish, made it possible to detect a gravitational wave for the first time on September 14, 2015 [DAM 19]. The recorded event occurred very far from our Milky Way: nearly 1.3 billion light years away! This discovery earned Thorne, 2 See, for example, http://www.virgo-gw.eu/ and https://www.ligo.org/.

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Weiss and a Barish the 2017 Nobel Prize in Physics, awarded at thee end of a scienntific life mobilizzed by the questt for gravitationnal waves [BAR R 16].

Figurre 3.14. First detection d of grravitational wa aves, named after a the day o of their discovvery, Septemb ber 15, 2014: GW150914 G [A ABO 16]. For a color version n of this figu ure, see www.iiste.co.uk/sigrrist/simulation2 2.zip COMMEENT ON FIGUR RE 3.14.– The e figure show ws the vibratioon signals siggning a gravitattional wave annd recorded att two LIGO ob bservatory sitess in the Uniteed States (Hanforrd, Washingtonn and Livingstoone, Louisiana).. Raw signals of o deformationss are the signature of gravitatioonal waves (top)). They are reco onstructed accoording to the prrediction of the general g relativiity model (midddle) and filtered d in order to prrovide evidencee for the variatioon of their freqquency with reespect to time (bottom). ( Dataa processing seerves the scientisst to thoroughlyy analyze the seqquence of cosm mic events that trrigger the gravvitational wave. The T measured deformation d is in i the range of 10−21: by compparison, the vibrration of a guitarr string, observvable to the nakked eye, is in the range of 10−2! The event is aanalyzed here ovver half a seconnd and involvees vibrations wh hose frequencyy varies betweeen 30 Hz and 500 Hz, a range correspondingg to that of ma any musical instruments, suchh as the guitar. The discovery of gravitationaal waves is thee fruit of one particular p interrnational collabooration: the histtorical publication from which h the figure is exxtracted is signeed by all scientissts who worked to develop meaasurement systeems and signall analysis methoods from gravitattional wave dettectors (source:: www.physics.a aps.org). Now wadays, simulaations provide data for artificcial intelligencee algorithms. IIn 2018, American researchers used the resultss of several hun ndred simulatioons of the fusionn of two black holes h to predict the characterisstics of the finaal black hole (itts mass, rotationn speed) and the shape of the grravitational wavve that this collision should prooduce [VAR 19]].

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Gravitational waves offer astrophysicists the opportunity to observe one of the most impressive physical phenomena in the cosmos. They open up a new interpretation of the Universe and the physical laws that humans have built in order to understand it – starting with the fall of an apple? Box 3.1. Newton’s equation

3.1.2. Observing the formation of celestial bodies The gravitational field plays an important role in the formation of black holes, and in order to understand the dynamics of these structures observed in the Universe and certain complex phenomena such as instabilities, researchers propose different physical and numerical models. The simulation then becomes a digital observatory to test many ideas or hypotheses explaining observations. Some of the physics at play in the dynamics of celestial bodies (such as planets or black holes) is that of plasmas, a state of matter made up of charged particles. It may be described by the equations of magneto-hydro-dynamics (MHD), which express the conservation of the mass, momentum and energy of particles, on the one hand, and the propagation of electromagnetic waves within the plasma, on the other hand. Two examples of simulations are proposed for the Rossby3 wave instability (Figure 3.15): – the first (top) corresponds to the evolution of a black hole and uses a calculation code developed by astrophysicists to study an instability evolving very quickly, in a few seconds; – the second (bottom) reproduces the formation mechanism of the heart of a planet, governed by similar physical mechanisms developing this time on longer time scales. From the simulations, astrophysicists develop radiation spectra: a curve of light that indicates the presence of a black hole – or any other entity studied. Compared to spectra from celestial observations, they allow researchers to propose explanations of the observed phenomena and to test their validity.

3 Carl-Gustaf Arvid Rossby (1898–1957) was a Swedish meteorologist. He was interested in the movements of large fluid scales in the atmosphere and the ocean. The wave instability that bears his name explains, for example, the characteristic shape of the Great Red Spot of Jupiter or that of cyclones. Found in the formation of black holes or planets, this mechanism, long known in meteorology and oceanography, is more recently studied in astrophysics.

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( Simulation of instability in (a) n the disc around a black ho ole (source: P Peggy Varnièrre, University of o Paris VII)

(b) Sim mulation of the e formation of a planet’s corre [VAR 06] Figurre 3.15. Exam mples of simula ation in astrophysics

To obbserve the forrmation of a planet’s p core, the simulatedd physical timee is a few million years y and requuires one monnth of calculattion. The evollution of instaabilities is significaant over severral hundred simulated s years. The calcuulation must rreproduce them andd, in order to be b reliable, noot artificially generate g them m, which happens when digital schemas are not n totally conservative. In n such a casee, the calculaation may e whose effect e is to po ollute the simu mulation. The ssimulated introduce numerical errors quantitiees are taintedd with errors that produce oscillations, without any physical meaningg.

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In order to validate the calculation method – and to ensure the stability of the numerical schemas – a simulation is started in a neutral initial state, free of disturbance. It is a matter of ensuring that this state does not change. The energy signal emitted by the plasma is then zero over the entire duration of the simulation: in the absence of an external effect, absolutely nothing happens and this is what is desired. If the numerical scheme is conservative, then the calculation method can be used to see the plasma evolve under the effect of physical phenomena, only contained in the equations – and not induced by numerical calculation errors. This is an issue that is also found in many other industrial applications. NOTE.– Conservative numerical schemes. A numerical method generally makes it possible to transform partial differential equations, involving variations in time and space of different physical quantities, into differential equations, involving variation in time solely. These concern the evolutions over time of the unknowns of the problem: a step-by-step calculation algorithm can be used to calculate them at different times (Chapter 1 of the first volume). Different numerical schemes may be implemented and they do not have the same digital properties. In some cases, there may be a loss of information during the simulation. Due to the time division, part of the mechanical energy of the simulated system is “filtered” by the calculation scheme. The calculated energy loss is more or less significant according to the diagrams and for most industrial simulations, it is known, controlled – and acceptable to engineers [BAT 82]. In other cases, such as astrophysics, meteorology or combustion, simulations extend over very long times, or with a large number of time steps. These require very robust digital schematics, not squandering the mechanical energy of the system they are calculating. Let us illustrate the subject with the simplest mechanical model: the harmonic oscillator – a ball attached to a spring, a yo-yo! Its mechanical energy is due to the movement of the mass (kinetic energy) and the deformation of the spring (potential energy). Away from its original position as the guitar string tensioned by the musician’s fingerboard, and left to its own devices without friction, it will vibrate regularly and endlessly. The mechanical energy of a harmonic oscillator depends on its position and speed. It is printed at the beginning of its movement and is preserved in the absence of losses of physical origin. All the initial conditions of the movement, the starting point, may be represented on two axes, position and speed (Figure 3.16).

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(a) Sche eme n°1

(b) Scheme n°2

(c) Scheme n°3 n Figu ure 3.16. Highllighting the pro roperties of cerrtain numerica al schemes [C CHH 08]

It has a given shappe: an ellipse or a circle (shown in blaack in the figuure). The surfacee of this figure represents thhe energy of the t oscillator. It is plotted oover time with position and velocity v coorddinates for diffferent simulaations (in whiite on the figure)) based on diffferent numericcal schemes. The ennergy conservaation propertiees are thus hig ghlighted: – Scheme S n°1 artificially a prroduces digitaal energy forr the oscillatoor whose movem ment it calculaates: the area of o the ellipse increases. i – Sccheme n°2 diigitally destrooys the energ gy of the osciillator: the area of the circle decreases. d – Sccheme n°3 preserves energgy: the area off the ellipse, which w can nevvertheless deform m, remains connstant.

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This theoretical experiment is used to test the properties of an energy-conserving simulation. The latter are essential to represent subtle physical phenomena, over long or even very long periods of time. For some industrial simulations, such as the rotation of helicopter blades, it is imperative to represent the evolution of mechanical energy as accurately as possible. Otherwise, the calculation would produce a result without any physical reality, at the risk of not anticipating critical phenomena, such as instabilities, that could affect the reliability and safety of an aircraft in flight. Only calculations based on a numerical scheme with the adequate properties can be used in these cases. The writing of robust methods digitally preserving physical properties refers to a current field of research based on Noether’s theorem4 [CHH 08]. It contributes to increasing the overall reliability of simulations: these theoretical advances will ultimately benefit engineers implementing simulations. 3.1.3. Predicting the mass of stars Stars play a fundamental role in our Universe. They synthesize elements essential to certain life forms (carbon, oxygen, iron, etc.) and they contribute to the in-depth renewal of the composition of galaxies throughout their lives. They emit light energy necessary for certain chemical reactions to occur and, during explosions

4 Emmy Noether (1882–1953) was a German mathematician who contributed to major advances in mathematics and physics. The theorem which bears her name stipulates that the symmetry properties encountered in some equations of physics are related to the conservation of a given quantity. A “symmetry” refers to any mathematical transformation of a physical system that lets the transformed system be indistinguishable to the non-transformed one. This means that the equations that describe the system are the same before and after transformation. For instance, Noether’s theorem indicates that whenever a system is symmetric with respect to translation, there is a conserved quantity that can be recognized as the momentum. Emmy Noether demonstrated her theorem in 1915 at the time Albert Einstein conceived the General Relativity Theory – and Noether’s theorem was a decisive contribution to Einstein’s work. Noether’s theorem set up the groundwork for various fields in theoretical physics and can also be applied in engineering sciences [ROW 18]. As a woman of her time, Noether struggled to make her way in science – a man’s world – and she had to seek the support of eminent scientists, such as David Hilbert, to pursue her academic career. Still, she was not allowed to teach using her own name, let alone received wages from this... She also had to face the disapproval of some of her male colleagues, sometimes expressed in a violent form: “No women in amphitheaters, science is a man’s business!” [CHA 06]. Emmy Noether proved them wrong… and is considered one of the most brilliant minds of the 20th Century.

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marking the end of acctivity of the largest ones, they emit a laarge quantity of matter U Thee properties off stars vary wiith their mass:: into the Universe. – Higgh-mass stars have a “hot” temperature, their lifespann is relatively short (on the scalee of the Univeerse!): up to a few tens of millions m of yeaars. Marked bby intense energy activity, a they burn gases by injecting turbulence into the Univverse and contributting to its radiiation. – Low-mass stars,, like our Sunn, have a “co old” temperatuure. Long-lastting, they nd generally host h planets – potential contributte to the stabiility of planetaary systems an life-bearrers! The distribution d off the mass of the different stars s makes itt possible, amoong other things, too understand the t history annd functioning g of the Univerrse. From obsservations of the coosmos (Figuree 3.17), the disstribution curv ve shows, for example, thatt the most frequent mass of starrs is about onne-third of th he solar masss (denoted 0.33 Mo). It m and beyond (to tthe larger decreasees quite quickkly below (too the lower masses) masses).

Figure 3.17. 3 Stellar de ensity map of our galaxy. Fo or a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 3.17.– Creatted in 2018 by y the Europeaan Space Agenncy using data from m the “Gaia” ” mission, the image represents a three-ddimensional m map of the stars obsserved in our galaxy, g repressenting the mo ost massive onnes, which aree also the warmestt and brightesst. The latter are a mainly loccated near theeir training siite, in the

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heart of the Milky Way. Regions of high stellar density are represented in pink and purple, intermediate density regions in violet and light blue, and low-density regions in dark blue. The map also shows areas of high concentrations of stardust, in green, and known clouds of ionized gas are identified by brown spheres. The map lists nearly 400,000 stars over a distance of 10,000 light-years from the Sun. Centered around the latter, the map represents the galactic disc observed from a point very far from our galaxy. With a database of the positions and trajectories of more than a billion celestial bodies, the “Gaia” mission is one of the most prolific to date, providing astronomers with detailed information (source:© European Space Agency/K. Jardin/www.esa.int). This distribution seems to change very little from one part of the galaxy to another, and even from one galaxy to another, while physical conditions, such as density, can vary considerably. Patrick Hennebelle used numerical simulation (Figure 3.18) to understand the origin of this distribution, while studying the case of the stellar cloud: “We have performed a series of calculations describing the dynamics of a collapsing stellar cloud of a thousand solar masses. By varying over large amplitudes, from 10 to 10,000 for example, different model parameters, such as density or turbulence intensity in the initial state of the cloud, or by modifying the laws of gas thermodynamics, we have studied numerous evolution scenarios and identified which physical parameters influence the dynamics of the stellar cloud”.

Figure 3.18. Stellar density calculations in a star cloud [LEE 17a]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.18.– The figure represents the density of stars calculated in a collapsing cloud. It is represented in color by increasing values from blue (low density) to green (high density). The red dots mark stars of different masses whose formation is observed during the calculation (source: © CEA-DAp).

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The result of the simulations first of all surprised the researcher, as the analysis of the calculations showed that thermodynamic phenomena explain the distribution observed on the masses of the stars. The gas state equation describes the radiation transfer processes that occur in the collapsing cloud; it controls the cooling of the gas, including its ability to remove excess gravitational energy. By varying the parameters of this equation, researchers have better understood the dynamics of the collapsing cloud. “My initial idea was that thermodynamics played a minor role and we made this discovery almost by chance! The simulations then helped us in interpreting the results and developing a theory to explain them”. The mechanism proposed after the analysis of the simulations predicts the correct value of the characteristic mass of the stars: it effectively leads to a stellar mass distribution in accordance with the observations (Figure 3.19).

Figure 3.19. Stellar density calculations [LEE 17b]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.19.– The graph shows the distribution of stars produced in the collapse of a cloud according to their mass and under different assumptions introduced in the simulations. The distribution of the mass of stars has a maximum value around a mass of one-tenth of the solar mass, close to that observed in the cosmos (source: © CEA-DAp).

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If simulation nowadays allows discoveries in astrophysics, it is difficult to attribute the sole merit to it: “The calculations allow virtual experiments for which two questions are asked: the validation and understanding of the physical phenomena at work in the observed systems. A discovery involves a chain as a whole: observations, simulations and their interpretations”. Simulation, which now plays an essential role in the development of knowledge in astrophysics, benefits from the advances of many digital disciplines: HPC computing techniques and AI algorithms are making their way into the astrophysicists’ toolbox [VAR 19]. In addition, some calculation methods originally developed by astrophysicists have more or less direct applications in the industry. This is the case with the so-called “SPH method”, for example, a particulate method initially invented to describe certain celestial dynamics. It is also used by engineers to solve flow equations under conditions where conventional methods encounter difficulties (Figures 2.1, 2.19 and 3.20).

Figure 3.20. Aquaplaning simulation [HEM 17]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.20.– This aquaplaning simulation helps to improve vehicle handling. The difficulty of the calculation lies in modeling the contact of the tyre on the road, which pinches a fluid blade. Most of the methods used for fluid mechanics simulations fail to reproduce aquaplaning. Based on the description of particles, the SPH method, initially developed to conduct astrophysical calculations, proves to be adapted to this situation.

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3.2. Geophysics Journey to the Center of the Earth is the third adventure novel published by Jules Verne [VER 64]. He recounts a scientific discovery – that of the depths of our planet, coupled with an initiatory adventure, that of the narrator of the story, the young researcher Axel Lidenbrock, who accompanies his uncle in his underground research – and emerges from this extraordinary experience. The novel was written at a time when geology was in full development. Extrapolating on the knowledge of his time, Verne’s imagination describes an Earth full of mineralogical and paleontological wonders (Figure 3.21): eternal diamonds, mushrooms or petrified trees, fantastic creatures – all species extinct from the surface of the globe (algae, fish or prehistoric monsters).

Figure 3.21. Illustration of Journey to the Center of the Earth [VER 64], plate no. 30, drawing by Édouard Riou (1833–1900) (source: www.commons.wikimedia.org)

Advances in geophysics at the beginning of the 20th Century made it possible in particular to draw up a map of the Earth’s crust that was more in line with reality, highlighting its dynamic nature. The theory of plate tectonics was validated by the international scientific community in the 1960s. It explains the constant movements of the Earth’s mantle, which cause earthquakes, eruptions and tsunamis in various parts of the world. Responsible for terrible human losses, as well as very significant material damage, these events have left their mark on humans and their places of life for many years to come.

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Figure 3.22. Age of the oceanic lithosphere [MUL 11]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.22.– The colors on the map represent the age of the ocean lithosphere. The most recent zones, formed at the level of oceanic faults, are indicated in red. The age of the oldest areas (represented in purple) is estimated at 280 million years. The areas in green correspond to an average age of 130 million years. The black lines represent the boundaries of the tectonic plates. The movement speeds of the plates are in the order of a few centimeters per year. The fastest movements, about 20 cm/year, are recorded in some regions of Southeast Asia – such as Papua New Guinea – and the Pacific – such as the Tonga-Kermadec archipelago (source: https://www.ngdc.noaa.gov). Over the past decade, digital simulation has become a widely used tool in geophysical sciences. Used by researchers in this discipline, it helps in the assessment of natural disasters risks. In the following, we will examine three fields of application: earthquakes, tsunamis and eruptions. 3.2.1. Earthquakes Italy is located in an area of intense seismic activity: the life of the geological layers of this region is surrounded by the Alps to the northwest and by Mount Etna to the southeast of the country, which are evidence of tectonic activity. Characterized by violent ground movements, with acceleration levels far exceeding the acceleration of gravity, an earthquake is perceptible in all three spatial directions and produces strong mechanical stresses on buildings, often leading to their destruction. On Monday, April 6, 2009 at 3:52 am, the country experienced a major earthquake near L’Aquila, a town in the mountainous region of Abruzzo. With a magnitude of 6.2, its human toll was terrible: more than 300 dead and 1,500

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wounded. The earthquake also destroyed many villages: about 40,000 buildings were demolished or severely damaged, affecting the lives of more than 70,000 people in the region. It is one of the most violent earthquakes recorded in Italy (Figure 3.23).

Figure 3.23. Recent seismic history of Italy (source: Emanuele Casarotti, National Institute of Geophysics and Volcanology). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.23.– The map shows earthquake records in Italy, classified by magnitude. This magnitude, representing the logarithmic energy released by an earthquake, is related to the damage it causes. A magnitude increase of 1 corresponds to a 30-fold increase in seismic energy.

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A chain of solidarity was set up after this disaster: providing relief, shelter, care and comfort. For the rescuers, a race against time is underway. The aim is to search for possible survivors in the rubble as soon as possible. Hours of work without sleep, in very difficult conditions – and let us not forget: this is a Western country, rich and organized, with extensive human and technical resources. In the case of such disasters, an additional danger comes from very strong aftershocks that can occur in the following days, on the same geological fault or on other faults located in the region. These aftershocks may endanger the lives of rescuers and people working in the debris. On Thursday, April 9, 2009, a very strong aftershock, magnitude 5.1, occurred and completed the destruction or damage of buildings in the L’Aquila region. Fortunately, residents had been evacuated from the heavily affected area since the first earthquake and the aftershock only caused material damage. In a discreet way, a geophysics researcher and numerical simulation expert helped to assess the risk of this eventuality by locating potentially dangerous ground vibrations. It was carried out using numerical simulations of possible aftershocks from the initial earthquake. After the first seismic tremors, seismologists gained accurate data on the disaster – for example, the coordinates of the epicenter of the earthquake as well as its approximate depth, and the accelerations recorded at different locations. They also became aware of the other geological faults in the impacted region and can speculate on how the original fault, or even others in the region, could fail. Dimitri Komatitsch tells us: “In the aftermath of the L’Aquila earthquake, I was contacted by seismologists from the National Institute of Geophysics and Volcanology (INGV) in Rome to build a numerical model of the region concerned. Using a calculation code that a community developed over the years to simulate ground vibrations in the event of an earthquake, I built such a model in less than 12 hours, feeding it with geological data from the L’Aquila region and INGV data on the first earthquake”. The calculations, sent to the Italian authorities for analysis, made it possible to obtain in a few hours the results of several aftershock hypotheses in the region for the days following the initial earthquake (Figure 3.24). The aftershock shown on the image was calculated in 2009. On 30 October 2016, the region experienced a seismic event whose global characteristics (magnitude, location of the epicenter and nature of the geological fractures) were very close to this calculation.

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Figure 3.24. 3 Scenario o for the L’Aqu uila earthquak ke aftershock:: in yellow and d red, the areas po otentially affeccted (source: calculations were carried out in 2009 b by Dimitri Komatitssch at the Centre Nationa al de la Recherche Scien ntifique in Fra ance and Emanuele Casarotti at the Nationall Institute of Geophysics G and Volcanologyy in Italy). e www.iste.co o.uk/sigrist/sim mulation2.zip. For a collor version of this figure, see

Second, the partiaal erasure of the t aftereffectts of such a disaster d is slow w. Before maged building gs must be loggged (Figure 3.25) and reconstruuction, an inventory of dam safe repaair options must m be soughtt. For some residents, r it taakes years to return to normal life.

Figure 3.2 25. Traces of the t earthquake e on buildingss in L’Aquila (s (source: ©Alain n Breyer/www w.alainbreyer.b be)

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In order to use simulation in emergency situations, it is crucial to perform fast and accurate seismic aftershock calculations and the code used by the researcher has two advantages: – a particularly efficient calculation method solves the equation of seismic wave propagation in geological layers. These are described by means of a viscoelastic behavioral law [TRO 08]. This equation, also discussed in Chapter 1 of the first volume, is similar to that used for the vibration of musical instruments. It yields accurate results for large-scale seismic models (that of a given region); – the computing power of a supercomputer, at the time a partition of nearly 500 computing cores of a machine, assigned urgently for these life-size calculations by GENCI in France. The development choices made on the seismic simulation code at the time of its development made it particularly suitable for porting to HPC computing means [KOM 11]. The improvement of this seismic calculation tool remains at the heart of geophysicists’ research today: “One of the main areas of development is a more detailed characterization of the basements. It is accomplished through seismic imaging, by comparing data recorded in situ after an earthquake and calculations made in these situations. The difference between the seismicity data recorded and their simulation allows for the iterative correction of geological layer models. To do this, the calculation codes constantly perform simulations: there are sometimes thousands of them for correcting a particular problem!”. Simulations obviously do not make it possible to predict the date of the seismic event, its location or its intensity. They contribute to the production of probable data for risk analysis. As a reminder, a few days before the major earthquake, a commission of Italian experts met in L’Aquila to analyze a series of earthquakes that had occurred in the region in the previous months. While they were obviously unable to predict the imminent arrival of a stronger earthquake, they made recommendations on the potential dangers facing the region at that time. For some Italian citizens, these were insufficient. After the earthquake, the seven scientists on this commission were found guilty of negligence in their seismic risk analysis. They were accused of giving too much reassuring information to the population, who could have taken measures to protect themselves. The experts were sentenced to prison terms and acquitted 2 years later on appeal. These trials have had a strong impact on the families of the victims of the earthquake and have also caused a great deal of misunderstanding and emotion in the international scientific community. These facts raise questions about the place and role of scientists in the prevention of natural risks, and about citizens’ expectations of experts and even the sciences.

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Legitimate in the obligation of means and in the search for proven errors, such as negligence or breaches of mandatory and legal procedures, these expectations can sometimes be disproportionate, even unrealistic, given the current capacity of science and scientists to predict with certainty certain events and their effects. This capacity often remains limited, as in the case of seismic risk: “The only current earthquake prevention measure is to identify areas at risk (L’Aquila was one), build buildings seismically (designed to withstand earthquakes) and educate people to take shelter at the very beginning of seismic movements...”5 Let us conclude this section by noting that the Earth shakes under the effect of tectonic movements as it also can under the effect of crowds –with a vibration energy that is nevertheless much lower [SIM 18]. During the 2018 football world cup, the vibrations generated by the jumps of joy of Mexican fans were recorded by the seismographs of the Mexican Atmospheric and Geological Research Institute6. 3.2.2. Tsunamis Hokusai, master of Japanese printmaking, was nearly 70 years old when he published his 36 Views of Mount Fuji in 1830. His sumptuous images are a true worship of the sacred mountain: it is present in an imposing way, or by becoming more discreet, in all the landscapes or scenes of life that the artist represents there. The first print in the series is probably Hokusai’s best-known print. The Great Wave [CLA 11] testifies to Japan’s ancestral vulnerability to tsunamis. On March 11, 2011 at 2:45 am, an earthquake of magnitude 9.0 occurred 130 km (81 miles) off the coast of Sendaï on Hinsu, the main island of the Japanese archipelago. This earthquake was the most devastating in Japan after the Kobe earthquake in 1995 (5,500 deaths). It was the fourth most intense earthquake ever recorded since the first measuring devices were deployed in 1900. The tsunami caused was the deadliest since the Hokkaido tsunami in 1993 (200 deaths). Images of the country’s devastation and the pain of its inhabitants left their mark on the entire world. The official report drawn up in February 2015 by the Japanese authorities indicated that 15,890 people were killed and 2,590 missing or presumed dead, as well as 6,152 injured in the country’s 12 prefectures. The earthquake and tsunami caused nearly $220 billion in damage in Japan and contributed to the

5 www.planet-terre.ens-lyon.fr. 6 Available at: http://iigea.com/sismo-artificial-por-celebracion-de-gol-en-mexico/.

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disaster at the Fukkushima I (D Daiichi) nucllear power plant – withh severe h of the country’s c popu ulation and ecconomy. consequeences for the health

Figure 3.2 26. An underw water earthqua ake can cause e a tsunami (source: © www.shuterstoc w ck.com). For a color version n of this figure e, see www.iste..co.uk/sigrist/s simulation2.zip p

COMMEN NT ON FIGURE E 3.26.– A tssunami is a train t of oceann waves geneerated by seabed movements, m thhemselves ressulting from an a earthquakee or eruptionn. At high depths, the tsunami wave has a very small amplitude inn the order oof a few a near thhe coast, it ca an take on a much m greater aamplitude centimetters. When it arrives and breaak into a turbuulent wall seveeral meters hiigh. The effects of thhe tsunami were w felt throu ughout the Pacific P Rim. IIt caused m on thee island of Haawaii, destroyying U.S. damage estimated at nearly $30 million Navy faccilities, and caaused more thhan $6 million n in losses to the fishing inndustry in the city of Tongoy, Chile – moore than 16,0 000 km from the epicenteer of the o a also revealed for the first time t the effeccts of the earthquaake. Satellite observations tsunami on the collapsse of the Antaarctic ice cap.

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The prevention of such disasters is based, among other things, on an observation of the state of the seas. In the Pacific Ocean, the DART (Deep-ocean Assessment and Reporting of Tsunamis) network consists of buoys that measure wave elevation and detect the formation of a tsunami. The data collected are used, for example, by various state agencies, such as NOAA* in the United States, to make predictions about the spread of a tsunami once it is detected. The models focus on the tsunami’s velocity (Figure 3.27) and the amplitude of the waves formed (Figure 3.28).

Figure 3.27. Estimated time for tsunami wave velocity induced by the Sendai earthquake in 2011 according to the National Oceanic and Atmospheric Administration (source: © NOAA/www.noaa.gov). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.27. – In the case of the Japanese tsunami in March 2011, the detection occurred about 25 min after the initiating earthquake and propagation calculations allowed the authorities of many countries bordering the Pacific Ocean to take measures to ensure the safety of the populations and facilities.

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Figure 3.28. 3 Tsunam mi wave heig ght induced by b the Senda ai earthquake in 2011 estimate ed by the National N Ocea anic and Atm mospheric Administration A (source: © NOAA//www.noaa.go ov). For a colo or version of this t figure, see e http://www.isste.co.uk/ sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 3.28.– The image i represeents a simulattion of the waave height generateed in the Paccific Ocean byy the tsunamii of March 111, 2011. The model is establishhed by NOA AA’s Pacific Marine Envvironmental Laboratory, using a calculatiion method adapted a to thiis type of eveent, and baseed on the usee of data collectedd by a networrk of buoys at sea. A tsuna ami spreads like l a “lonelyy wave of infinite wavelength”: w ms to move ass a whole. Thee propagationn speed of the wave seem a wave varies v globallly like the squuare root of th he product off gravity and depth: in deep water, the speedd of a tsunami can reach nea arly 800 km/hh while not excceeding a few tens of centimeterrs in height. The T largest wa aves are locateed in the areaa near the c of Japan n. Their ampliitude decreasees as they epicenterr of the earthqquake off the coast spread too the deepest regions of thee Pacific Ocea an. They breaak when they eencounter shallow waters near the coast. Thhe energy carrried by the waves w weakenns as they way from wherre they originnated: the effeect of the tsunaami is less deevastating move aw off Haw waii than it is on the Japanese co oast (source: https://www w.tsunami. noaa.govv/). Tsunnamis can bee caused byy geophysical events othher than eartthquakes: underwaater volcanic eruptions e or issland volcano collapses aree other possiblle causes. While nuumerical simuulations nowaadays make it possible to prroperly accouunt for the propagattion of tsunam mis, one of the major uncerrtainties in the calculation is that of the condditions under which they are a generated. What energyy is transporteed by the collapse of an island volcano slope? Is it enoug gh to trigger a major tsunaami? This

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risk is real r in differrent parts of the world an nd for many volcanic islaands that experiennce regular eruuptive episodees (Canary Isllands in Spainn, Hawaii in thhe United States, Reunion R Islannd in France, Java in Indo onesia). The Cumbre C Viejaa volcano (Figure 3.29) 3 on the issland of La Paalma in the Caanary Islands attracts a the atttention of scientistss because of itts position andd geology.

Figure 3.29. The Cumbre Vieja vo olcano in the Canary C Islandss last erupted in 1971. o occur and d can it cause a volcano slop pe to collapse at sea, When will the next one owed by a tsun nami? (source e: www.commons.wikimedia a.org, GoogleM Map) follo

In 20001, two geopphysical researrchers, the Am merican Stevenn Ward and thhe British Simon Day, D publishedd a study on thhe risk of a co ollapse of a paart of the Cum mbre Vieja during an a eruption. According too their calcullations, this event would create a tsunami whose effectss would be felt across the Atlantic A Ocean, as far as thhe Florida R 01]. Their aarticle had coast, annd would also affect Africa and Western Europe [WAR a certainn impact on the t general puublic and the risk of the volcano’s v colllapse was sometim mes presented in i a caricatureed manner, as if by a sensattionalist press invoking biblical predictions p [B BEI 17]. Afterr its publicatiion, the concclusions of Ward W and Dayy’s study werre widely discussed by the scienntific communnity. The risk that the two researchers r highlighted with theeir simulation proved overeestimated, as the calculatioons are basedd on very conservaative assumpttions – they assume, for example, thaat half of thee volcano collapsess during an erruption, a hypoothesis that so ome geologistss dispute [DEL 06]. The scientific coontroversy haas highlighted d the need to better control the mulations, in particular p by refining moddels of volcannic debris hypothesses of the sim flow. Thhis is achieveed through more m accurate experimentall data and caalculation codes, allowing a a moore realistic assessment a of the risks of a collapse and of a tsunami [ABA 12].

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Sylvain Viroulet, a young researcher and author of a PhD thesis on the generation of tsunamis by geophysical flows [VIR 13], explains how a simulation based on experimental campaigns is constructed: “I have worked on different landslide models to understand the dynamics of debris flow. My research consisted in developing an experimental device and a numerical model. Validated on the controlled configurations that the experiment allows, the simulation enables extrapolations to situations similar to those encountered in the field. Using numerical calculation, it is possible to study a wide variety of scenarios of a volcano’s collapse in the ocean, which allows for a better characterization of the wave thus created and the intensity of the tsunami it may generate”. In the laboratory, the aim is to reproduce different configurations representative of landslides caused by the flow of a debris stream or by the impact of debris on a static cluster (Figure 3.30).

(a) Jet flow

(b) Impact on a debris pile

Figure 3.30. Experimental study of the flow of debris encountering a bump

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COMMENT ON FIGURE 3.30.– The figure shows photographs of debris flow experiments in two situations. On the left, a jet flow: the materials encountering a bump detach from the ground and follow a parabolic trajectory, before touching the ground again. Conditions of “stationary flow”, independent of time, then establish themselves. On the right, a debris flow is triggered by the impact of materials on a cluster upstream of a bump. After contact, there is a sudden decrease in the overall velocity of impacting particles and an increase in the thickness of the flow. These conditions propagate upstream of the resting area until the flow reaches an equilibrium position and then develops a stationary flow [VIR 17]. The experiments allow us to understand the physics of granular flows, involving different phenomena, among which erosion and deposition of matter, the presence of gas in the fluid bed or the segregation of particles according to their size – the more they are mixed the less they mix, so that large particles form the front of the flow and constrain it by retaining the smallest particles. “With the computer, there are several options available to researchers and engineers. Particulate methods consist in solving Newton’s laws grain by grain, taking into account interactions with a surrounding fluid, the latter being represented by the Navier–Stokes equation. However, computation times are very long with this type of approach and researchers are developing methods from fluid mechanics to apply these simulations to geophysical cases. The challenge is then to represent the granular rheology using an equivalent friction”. In Navier–Stokes equations, for example, this granular rheology can be represented by a viscosity that changes with the pressure and shear effects observed on moving grains [LAG 11]. The avalanche of a column of volcanic debris is, to some extent, accessible by simulation (Figure 3.31), but the entry into the water is not yet well represented: this physical ingredient is still missing in current models. A forthcoming eruption of Cumbre Vieja, like other active volcanoes on the planet, is certain. The risk of a Great Wave cannot be scientifically ruled out in such circumstances. The use of simulations based on a physical analysis allowed by laboratory experiments thus contributes to evaluating the consequences of different collapse scenarios in a more realistic way than the apocalyptic predictions, which some may sensationally claim.

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Figure 3.31. Simulation of an avalanche of volcanic debris [KEL 05]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 3.31.– The figure shows a simulation of the debris avalanche that occurred in 2010 on the Scopoma volcano in Chile. It is carried out with the VolcFlow code7. This calculation tool can be used to determine the rheology of pyroclastic flow or debris avalanches. It allows for a visualizaton of the surface deformations of these flows and an interpretation of their physics. It can also be used to simulate the formation and propagation of mudslides or tsunamis. The code is made available by its developers to a wide scientific community, particularly in Asian and South American countries that do not have the research resources necessary for their development. Using this code, French and Indonesian researchers studied a scenario of a landslide of the Krakatoa volcano in Indonesia in 2012. Their calculations described the characteristics of the tsunami that would result from an awakening of the volcano [GIA 12]. Such a tsunami did indeed occur in December 2018 (source: Karim Kelfoun, University of Clermont-Ferrant). 3.2.3. Eruptions The second print in Hokusai’s series, 36 Views of Mount Fuji, depicts the volcano in all its glory [BOU 07]: a red pyramid rising into the sky at a quivering dawn, coloring the sky a royal blue and dotted with cloud lines striating the atmosphere. The slopes of the volcano, zebra-striped at its peak with snowflows, soften at its base to a gradation of reds and oranges mixed with the greens of a sparse forest (Figure 3.32). There is no reason to believe that there is any danger behind this peaceful landscape: we contemplate Mount Fuji, forgetting that it is a volcano, still considered active today, although its latest eruption only dates back to the 18th Century. 7 Available at: http://lmv.uca.fr/volcflow/.

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With more than 110 active volcanoes, Japan is located in the “Pacific Ring of Fire”, a vast area that contains most of the world’s earthquakes and volcanic eruptions. In 2018, a Japanese government study indicated that an awakening of the volcano could cause the accumulation of 10 centimeters of ash in central Tokyo, 100 km from Fuji. These ashes would make roads impassable, blocking transport and thus the city’s food supply [ICH 18].

Figure 3.32. Red Fuji, Katsukicha Hokusaï (1760–1849), second view of the 36 Views of Mount Fuji, 1829–1833 (source: www.gallica.bnf.fr)

Volcanic eruptions have both local and global consequences, often dramatic for populations, as these two examples show: – In 1991, the eruption of Mount Pinatubo in the Philippines was one of the most significant of the 20th Century. The surroundings of the volcano were profoundly disturbed: the mountain was losing a significant amount of altitude and the surrounding valleys were, over hundreds of meters, completely filled with materials resulting from the eruption. The forest on the mountain slopes was completely destroyed, the animal species that used to live there died. With a death toll of nearly 1,000, it made the country pay for a heavy human and economic loss. – In 2010, the Icelandic volcano Eyjafjöll projected a large plume of water vapor, volcanic gases and ash. Driven by the prevailing winds that brought them

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down to continental Europe, it caused major disruptions in global air transport for several weeks. Volcano activity is closely monitored by the security authorities of the many countries affected by their potential eruption. Karim Kelfoun is a researcher at the Magmas and Volcanoes Laboratory, Clermont Ferrand Observatory of Earth Physics, Clermont Auvergne University. He develops tools for simulating volcanic flows [KEL 05, KEL 17a, KEL 17b] used for research and risk analysis purposes: “Volcanic eruptions are obviously rare and dangerous and laboratory experiments exist only for the study of the physics at stake. These are confronted with scale problems that do not make them relevant for field interpretation. Only numerical simulations may be used to study different eruption scenarios, such as changes in crater topography or slope topography, and they assess the consequences of assumptions made by volcanologists. Calculations help to refine volcanic risk maps, for example for predicting trajectories and potentially destroyed areas. Numerical tools are becoming more widespread in this field, particularly because of the increasing demands that populations at risk make on their country’s security authorities. The simulations are currently quite accurate, however, some parameters of the calculations are based on observations, not on physics. This limit can be problematic when it comes to predicting eruptions with rare characteristics. The forecast keeps an approximate aspect because the characteristics of the next eruptions are not known in advance”. Numerical modeling is based on the conservation equations of the different physical quantities monitored over time. The simulation consists of solving these equations using a numerical method describing the mass and momentum fluxes and the forces exerted on the calculation cells of which the model is composed. The main difficulty is to model the rheology of flows: classical models, describing friction within the material, are not adapted to volcanic materials. Most of the research work is carried out in this field by comparing different theoretical rheological models with field observations. In addition, the numerical methods used must be “stabilized” and “optimized”, thus the calculation code: – continually checks that the elementary physical principles are respected, for example that flows do not go up the slopes: this effect is obviously impossible in reality, but a calculation can artificially produce it8;

8 As we mentioned in Chpater 4 of the first volume, the question as to whether a simulation correctly renders physical phenomena applies to all kinds of calculations.

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– uses efficient algorithms to perform simulations in the shortest possible time. Depending on the case, the calculation times can take between a few minutes and 1 hour on a standard computer. It is by looking into the past, i.e. by analyzing field data collected during known eruptions, that researchers try to predict the future through their simulations. Numerical models are built from the topographic and geological surveys of volcanoes, and it is crucial to know them beforehand in order to carry out simulation risk studies. “Geophysical monitoring, carried out by volcanological observatories, is also very important: it provides precise data, useful for calculations”, explains Karim Kelfoun. An example of a simulation is presented below for the Indonesian Merapi volcano, which erupted several times in the 20th Century (Figure 3.33).

Figure 3.33. Eruption of the Merapi volcano in 1930

COMMENT ON FIGURE 3.33.– The photograph is an aerial view of the Indonesian Merapi volcano, taken during its eruption in 1930. A volcanic plume escapes from the crater at its top. The latter is partially blocked by a lava dome, visible as the dark mass under the crater (source: www.commons.wikimedia.org). The simulation performed is that of the 2010 eruption (Figure 3.34) and according to its author, it makes it possible to properly reproduce the major phases of the eruption, and to understand qualitatively the phenomena involved. However, the code has serveral limitations of modelling, which researchers are currently working on.

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“In reality, the role of temperature and atmospheric ingestion in flow, which would explain its very high fluidity, is not yet rigorously described in the simulations. In the laboratory, the calculation code reproduces experiments to study the effect of air on flowability. Our current research aims to better understand these mechanisms in order to quantify them at scale and under field conditions...”

Figure 3.34. Simulation of the 2010 eruption of the Merapi volcano in Indonesia with the VolcFlow code [KEL 17b]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

As a conclusion, let us remark that the calculation code used for these simulations is developed in France by researchers from the Magmas and Volcanoes Laboratory, located in the heart of the Auvergne Volcanoes National Park: with mountains somehow as majestic as Mount Fuji – but less threatening, since they have long been plunged into a long volcanic sleep.

4 The Atmosphere and the Oceans

In the late 1960s and early 1970s, astronauts on American missions to the Moon had the privilege of viewing the Earth from space. On December 24, 1968, Bill Anders participated in the Apollo 8 mission and witnessed a rising of our planet from the Moon. Earth Rise depicts a blue dot timidly drawing itself on the horizon of an arid and dusty space. Four years later, Eugene Cernan (1934–2017) photographed the Earth from the Apollo 17 mission ship. His image, Blue Marble, is dated 1972 and is the first where our planet appears on its sunny side and in its entirety. The American astronaut is said to report on his experience in these terms: “When you are 250,000 miles (about 400,000 km) from the Earth and you look at it, it is very beautiful. You can see the circularity. You can see from the North Pole to the South Pole. You can see across continents. You are looking for the strings that hold it, some kind of support, and they don’t exist. You look at the Earth and around you, the darkest darkness that man can conceive...” [www.wikipedia.fr]. His words illustrate the awareness of the finiteness and fragility of our lives and evoke that of the planet that hosts us. Reported by many astronauts and referred to as the Overview Effect, it accompanied the development of environmental movements in the late 1970s. Images from space, together with other observations, contribute to raising awareness of the environmental and energy challenges facing humanity at the beginning of the 21st Century. Numerical simulation has become a tool for understanding and predicting with increasing precision many phenomena occurring in the oceans and atmosphere: this chapter aims to provide an overview, ranging from weather forecasting to climate change modeling.

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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4.1. Meteorological phenomena, climate change In 2015, NASA unveiled a second image showing the Earth in its entirety1. It was taken by DSCOVR, a satellite that observes our planet and its climate, placed at the Lagrange point L1 (Chapter 3). That same year, Italian spacewoman Samantha Cristoforetti photographed Maysak’s development and progress from the international space station (Figure 4.1).

Figure 4.1. Super Typhoon Maysak photographed by Italian engineer and pilot Samantha Cristoforetti on March 31, 2015 on board the international space station (source: © European Space Agency)

A category 5 typhoon (the highest), Maysak crossed the Federated States of Micronesia in the South Pacific, then the Philippines, and swept them with strong winds blowing at over 250 km/h. It also causing the formation of waves higher than 10 m. Forecasting such meteorological phenomena, among the most spectacular, or others, those of our daily lives, is accomplished by means of numerical simulations based on equations and data. Forecasts are nowadays achieving greater accuracy, made possible by the development of efficient calculation methods. Numerical simulations are also used by researchers to study the Earth’s climate and try to predict its evolution. Climate depends on how the energy received by the 1 Available at: https://earthobservatory.nasa.gov/images/86257/an-epic-new-view-of-earth. From these images, French engineers Jean-Pierre Goux [GOU 18] and Michael Boccara developed Blue Turn. An application that offers everyone a unique, intimate and interactive experience of the earth totally illuminated and rotating, seen from space. A numerical simulation of the visual experience reserved until now for astronauts only (available at: www.blueturn.earth).

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Earth from the Sun is absorbed by our planet, the oceans and the atmosphere, or reflected back into space by the atmosphere. The dynamics of the atmosphere and the oceans are linked by their energy exchanges. The latter are responsible for an intrinsic variation in climate, to which are added two major effects, driven by aerosols and gases in the atmosphere (Figure 4.2).

Figure 4.2. Emissions of substances into the Earth’s atmosphere (source: © NASA/J. Stevens and A. Voiland). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 4.2.– This image, produced on Thursday, August 23, 2018 by the NASA Earth Observatory, shows the emissions of different components into the atmosphere: carbon dioxide in red (resulting from human activities, or natural hazards, such a huge fires – as occurred, for instance, in 2018 in the United States or in 2019 in Brazil), sand in purple and salt in blue. Aerosols are suspended particles, emitted, for example, during natural phenomena, such as volcanic eruptions or storms (in Figure 4.2, salt and sand, for example), or by human activities. They tend to cool the atmosphere by contributing to the diffusion of solar energy: for example, a decrease in global temperatures was observed after the eruption of Mount Pinatubo in 1991. For 2-3 years, it interrupted the global warming trend observed since the 1970s [SOD 02]. Some gases in the atmosphere (water in the form of vapor in the clouds, CO2 or other chemical compounds such as methane or ozone) tend to warm the atmosphere. Absorbing light in the infrared range, they block the re-emission into space of the thermal energy received on the ground under the effect of solar radiation. Without this greenhouse effect, our planet would simply be unbearable, with an average temperature of around −18°C [QIA 98].

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Whille the effect of o aerosols tennds to disappeear quickly (w within a few m months or years) when w they fall to the grouund, the influence of greennhouse gases is much longer. It I is also delayyed from theirr release, as th hey persist lonnger in the atm mosphere (a few years y or decaddes) and accum mulate there – thus gas em missions, and eespecially CO2 emissions, receivve special atttention. The latter l are the result of botth natural cycles (ee.g. plant and tree growth) and human acctivities, and it is a well-knnown fact that releeases from various v sources have steaadily increaseed over the past two centuriess (Figure 4.3)..

Figure 4.3. CO O2 emissions frrom different sources s (sourcce: Our World d in worldindata.org g/co2-and-other-greenhouse e-gas-emissio ons). Datta/https://ourw Forr a color versio on of this figurre, see www.is ste.co.uk/sigriist/simulation2 2.zip

Thuss, in 2017, thhe concentrattion of CO2 in the atmossphere near tthe Earth reached a record valuue of 405 ppm m, the highestt in recent atm mospheric history. The m ice su urveys can goo back nearlyy 800,000 values estimated usinng polar or mountain years: thhey also indiicate that thee 2017 level is unprecedeented over thhis period [BLU 188]. Channges in tempeeratures on Eaarth mainly deepend on thesse effects of abbsorption or reflecction of solaar energy (innfluenced by aerosols annd greenhousee gases), terrestriaal thermal emiissions, and exxchanges betw ween the oceanns and the atm mosphere. The mosst recent data show that thee average tem mperature on Earth E has beenn steadily increasinng since the 19960s (Figure 4.4). 4

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Figure 4.4. 4 Evolution of the average temperature e at the Earth’’s surface from m 1850 to 2017 (source: ( Ou ur World in n Data/https s://ourworldind data.org/co2-a and-othergreenhou use-gas-emisssions). For a color version n of this figure e, see www.isste.co.uk/ sigrist/sim mulation2.zip.

COMMEN NT ON FIGURE E 4.4.– The figu ure representss the evolutionn of the averagge global temperatture, in termss of deviation from f a refereence (here, thee average tem mperature observedd over the latee 19th Centuryy). The data presented p are the result of sstatistical processinng: the red cuurve represents the median value of the data d (the tempperatures are dividded into two sets s of equal im mportance) an nd the gray cuurves the tempperatures below 5% % of the minimum values and above 5% % of the maxximum values (extreme values are a thus elim minated). Thee average va alue, obtaineed from tempperatures measureed at differennt stations, by b definition masks temperature dispaarities in differentt parts of the planet. p “Globbal warming” ” refers to the steady rise of Earth’s average temperature. To what w extent doo CO2 emissioons, and moree broadly all substances s relleased by human activities, a influuence this clim mate change? Based on maathematical moodels and reflectingg the current understandinng of climate mechanisms, numerical sim mulation, developeed and refinedd since the 1970s, is a too ol that scientiists use to annswer this questionn. 4.2. Atm mosphere an nd meteorology The semifinal s of thhe Rugby Woorld Cup, Octo ober 13, 20077, Stade de Fraance, pits the startiing 15 Englissh ‘Roses’ against 15 Fren nch ‘Blues’: thhe rivalry bettween the

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two nations is no longer historical or political, it is that particular day, sporting! For 80 minutes, the players ran after an oval shaped ball that was more capricious than usual. Carried by strong winds, it condemned them to a game entrenched in the mud. Wet by frivolous rain, the passes appear blurry. Only one try is scored in the game, feverish and uncertain, while other points are obtained by penalties. With two minutes remaining, the whites camped in front of the blue poles despite the bad weather and Jonny Wilkinson – one of the most talented players of his generation – made a memorable coup de grâce to the French team, a drop perfectly adapted to the weather conditions. For England’s number 10, it was not the first time he had tried it. In the final of the previous competition against Australia, he gave his team a world title with a kick in the last seconds of a match, at the end of which the outcome was just as uncertain. Jonny Wilkinson was personally interested in quantum mechanics, out of intellectual curiosity. For the French physicist Étienne Klein, with whom he exchanged at a conference organized at the École Nationale Supérieure de Techniques Avancées [WIL 11], this outstanding sportsman had, through his practice of rugby, intuitively understood certain concepts of quantum mechanics. Conquest by moving backwards, ball with random rebounds, part of the interpretation of the game phases by a referee-observer who influences the progress of the current experience: rugby is also a sport that defies classic mechanics. If the weather conditions had been different on that unfortunate semifinal day for the French, would the match have been different? 4.2.1. Global and local model Whether in sport, agriculture, fishing, industrial production, transport, tourism and leisure, our dailiy life is largely conditioned by the vagaries of the sky, clouds or winds. Knowing the weather in a few hours or days, with a sufficient level of reliability to avoid inconvenience, is an increasingly important issue for many economic sectors. Wind speed, air temperature and pressure, atmospheric humidity are the quantities that weather forecasts seek to calculate at different scales. Météo-France contributes to the development of models that meet this objective. A global model reports on changes in the atmosphere and is based on various assumptions. In particular, the Earth is supposed to be perfectly spherical, covered with a mantle of several atmospheric layers, with a significant thickness (up to 100 km above sea level, i.e. 25 times the altitude of Mont-Blanc!). The global model provides information on weather conditions over the entire surface of the planet: these are used to provide information for local models, for example, at the scale of a country.

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Cloud formation, air mass flow, sometimes spectacular as in a storm or typhoon: meteorological modeling uses fluid mechanics equations. The simulations obtained with the global model are based on a mesh of the atmosphere using elements or volumes whose size determines the accuracy of the calculation (Figure 4.5).

Figure 4.5. Meshing of the atmosphere (source: © ISPL/CEA-DSM). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

For the global model, the elements have a dimension of just under 50 km on each side, for the local model, about 1–10 km. The Earth’s surface area is about 515 million km2: it is therefore covered by 5 million elements within 100 km2. For local models, the volumes are about 1 km apart. The surface area of France is 550,000 km2: as many elements of 1 km2 are used for the simulations, 100 times more to take into account the variation of physical quantities with altitude. A meteorological simulation thus calls for between 5 and 500 million elements (by comparison, an industrial simulation of a ship or aircraft may require a few million elements). On each element, there are many quantities to calculate: temperature, pressure, humidity and velocity in three directions. Nearly, 1 billion pieces of data to calculate at different times during the simulation. An additional difficulty arises for simulations: the equations of fluid mechanics represent different phenomena, such as the advection and propagation of physical quantities, whose evolution over time takes place at very different paces. In order to correctly represent these phenomena, it is necessary to use a time step that is smaller the higher the spatial resolution. This ensures the stability of the calculation. When the forecasts extend over a 10-day period, simulation times would become

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prohibitiive. The calcuulations then use u appropriaate algorithmic techniques, allowing these pheenomena withh contrasting dynamics d to be simulated seeparately. Counntry-scale sim mulations (Figuure 4.6) find data from thee global model useful, for exam mple, to determ mine boundaryy conditions (i.e. ( the meteoorological connditions at the edgees of a region)) and also useeful for local models. In paarticular, theyy describe the evollution of areaas of high orr low pressurre and all rellevant inform mation for weather reports: preseence and compposition of clo ouds, storms, rain, r snow andd fog.

Figure 4.6. Numerical simulation of a cyclone off the island ersion of this of Madagasscar (source: © CERFACS). For a color ve figu ure, see www.iiste.co.uk/sigrrist/simulation2 2.zip

o which to base its callculations. Thhe initial Eachh simulation needs data on conditionns give the most accuraate possible representation r n of the statte of the atmosphhere at the begginning of thee simulation. Data D assimilaation makes itt possible to determ mine them. Convventional meteeorological daata comes fro om the historical network oof ground stations or observatioon satellites – the latter no owadays provviding the buulk of the f forecastinng. They are supplementedd by opportuunity data informattion needed for obtainedd from shippinng and airline companies. Winds, W clouds, humidity, tem mperature and air pressure p also influence the transmission of informatioon on various systems, such as GPS. By obsserving the efffects using models, m it is possible to trrace their g based on the exppected sound qualities: cause – such as definning a guitar geometry o “inverse methods”. m Thesse indirect datta have compplemented scientistss also speak of conventiional data for the past 20 yeears or so.

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The quantities measured directly or estimated indirectly represent 5–10 million data: a significant quantity and yet insufficient to be used by simulations, which require nearly 1 billion! In order to complete the missing information, data assimilation uses the results of previous numerical simulations. This combination of collected and calculated data makes the particularity of a calculation method and code developed by Météo-France, in partnership with the European Centre for Medium-Range Forecasts. Data assimilation is an optimization problem: the state of the atmosphere is represented by a vector, a collection of calculated physical quantities, making the assimilation error as low as possible. In mathematical terms, such a problem is ( ). Ω represents the set of possible values for the quantities . written as ∈

measures the sum of the difference between the state being searched and the observations, on the one hand, and the difference between the same state and the previous numerical simulation, on the other hand. The difficulty is to find a minimum value for a function that depends on 1 billion variables! In order to find the such value, mathematicians use methods similar to those experienced in the sensitive world. Like a skier who runs down a slope looking for the most optimal path in terms of movement and disruption, thus adapting to the terrain, a descent algorithm rolls toward the lowest point of an uneven surface (Figure 4.6 in the first volume). In a few iterations, it makes it possible to find a minimum value for a mathematical function – sometimes depending on a very large number of variables. In addition, data assimilation techniques, coupled with the computational power applied to simulations, make it possible to perform emergency calculations, for example to predict intense and sporadic climatic phenomena, such as heavy rainfall. Using simulation and data assimilation, Météo-France carries out four daily forecast cycles for the global model, at 12:00 pm, 6:00 am, 12:00 am and 6:00 pm. For 4-day forecasts, which we have access to, for example, with an Internet application, calculations take 1 hour 30 minutes to assimilate data and 30 minutes to perform a simulation. An achievement performed every 6 hours! In recent years, these forecasts have been accompanied by a confidence index. The latter is a sign of an evolution in methods, made possible by increasingly computing capacities and by an evolution in computing methods. They now integrate uncertainties in the input data and assess their influence on the outcome of the forecast. This more probabilistic conception of simulation is one of the avenues for innovation in numerical methods in meteorology – as in other fields. The methods will have to evolve further, for example, by integrating the advances of Big Data [BOU 17]. Simulations and observations, but also traces of each other’s digital activities with the connected objects: stored, collected and

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processed by Météo-France, data related to weather and climate await the next algorithmic innovations to deliver their information and contribute to the development of new prediction methods, such as real-time information or warning devices, etc. 4.2.2. Scale descent The Route du Rhum is one of the prestigious solo sailing races and its progress is fascinating beyond the circle of regatta lovers. In 1978, its first edition was won by Canadian skipper Mike Birch. Departing from Saint-Malo in France, he reached the finish line in Guadeloupe after 23 days, 6 hours, 59 minutes and 35 seconds of racing, only 98 seconds ahead of his pursuer, the French skipper Michel Malinovski (1942–2010). Forty years later, the same scenario seems to be emerging: for the 2018 edition, the Frenchmen François Gabart and Francis Joyon are in the lead off Guadeloupe. At this stage of the race, weather data are crucial for sailors. On November 11, 2018, French meteorologist Yann Amice, founder of Metigate, simulated wind conditions around the island (Figure 4.7). For sailing specialists, the calculation suggests that the finish of the race presents many difficulties for skippers – will the finish be as competitive as in 1978? The 2018 race turned out to be different, perfectly illustrating the aphorism attributed to Niels Bohr in the first volume… Let us take a look at the simulation of wind conditions in 2018. It is carried out on a square area of 180 km, composed of calculation cells with 3 km on each side – a resolution which is essential in order to generate useful data for navigators.

Figure 4.7. Simulation of wind conditions around: the wind scale is indicated in knots (source: www.metigate.com) For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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Blandine L’Hévédder, an expert in weather an nd climate sim mulation, contrributed to the calcuulations: “Thhese simulattions are baased on ‘hig gh-resolution’’ meteorologgical techhniques: the aim a is to produuce realistic data d in given geographical g aareas witth high accuuracy. Typicaally, calculattions are peerformed withh a resoolution of aboout 1 kilometeer – and in so ome cases, it may m be less! The calcculations aree based on ‘downscaling g’ techniquess: starting ffrom metteorological data at a reesolution of 25 kilometeers, we simuulate succcessively the meteorologiccal conditionss on domains whose resoluution deccreases: 15 killometers, 3 kilometers... theen 1 kilometer. At each step of the calculation, we w use the ressults obtained at the upper scale s to set upp the ulation of the current c scale.”” inittial and bounddary conditionns of the calcu This scale desceent is carriedd out in step ps of resoluttion (Figure 4.8), the calculatiion taking placce in an immuutable sequencce.

Figure 4.8. 4 Downscaling principle: local simulatio on on the Marrseille region b based on global data on the South-East S of France F (sourc ce: www.metig gate.com). Forr a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 4.8.– The fiigure schemattically represe ents the princciple of a downscaaling: from a global meteoorological sim mulation result, for example with a resolutioon of 25 km, it i is possible to t obtain simu ulations at finner scales, forr example with a reesolution of 3 km. “Thhe first part of o the calculaation is that of o fluid dynaamics: it invoolves solvving the flow w equations (N Navier-Stokes equations) onn a 3D mesh and calcculating the pressure, vellocity and temperature fieelds. Indeed, the exppression of hoorizontal and vertical v variattions of the various v quantities,

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as well as that of the transport of these quantities by the wind, involve values in the neighboring meshes. The second part of the calculation is that of the physics of the atmosphere. Radiative phenomena (radiation, absorption, diffusion by clouds and gases in the atmosphere), and socalled ‘sub-grid’ effects (evolution of turbulence, formation of water drops, interactions related to friction with the ground induced by the presence of vegetation, construction, etc.) are represented. These phenomena depend on different factors that the models translate into equations called ‘parameterizations’. This calculation step takes place along the meshes of a vertical column and is regularly inserted between the fluid dynamics calculation steps. Carried out on average once after five dynamic steps, this process makes it possible to describe, for example, the rainfall or the turbulent transport of water vapor evaporating on the ocean surface. Similarly, the ground effect, which may be characterized in particular by friction, influences the flow profile up to an altitude of nearly 1,000 meters! It is essential to represent it and to do so, we use data from field surveys.” Different models operate during this last stage and all the “art of prediction” of the experts is mobilized in order to achieve the most accurate modeling possible. A constraint: that of calculation times! “Calculation techniques are limited by an essential constraint: the step of temporal resolution is imposed by spatial resolution. In particular, a numerical condition requires that the calculated information must not propagate at a speed greater than that of a space mesh over a calculation time step – otherwise, the simulation loses all meaning, indicating a mathematical result (the latter is known as the ‘Courant-Friedrich-Lewy condition’, after the mathematicians who helped to understand and formalize it). Thus calculations with low spatial resolution take the longest time and may only be accessible with supercomputers. Simulating 48 hours of weather over a 60-kilometers-side region with a 1 kilometer resolution requires only 30 minutes, using 32 computing cores! According to the same principle, it is possible to descend to smaller scales: up to 50 meters, 10 meters, etc., using other types of models.” The weather tomorrow or in 10 years’ time is gradually becoming less elusive, but the result of the next Rugby World Cup or the ranking of the next sailing race remain uncertain until the final whistle blows or the arrival at the port!

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4.3. Oceans and climate After the Second World War, a world dominated by the United States and the Soviet Union emerged. In April 1961, the first man who reached in space was Russian. In July 1969, the first men to tread the lunar ground were American. A Cold War legacy may be embodied in the race between the two powers to space. Communications, transport, meteorology, and observation of the Earth: nowadays, a large part of humanity benefits directly from this conquest. International space missions have made it popular, thanks in part to outstanding personalities, including those mentioned at the beginning of this chapter, or more recently the likes of French astronaut Thomas Pesquet [MON 17, PES 17]. The Silent World, the realm of the deep ocean, can arouse the same enthusiasm as the conquest of space, with the oceans being, for some, the future of humanity. In 1989, Canadian filmmaker James Cameron, passionate about the seas and oceans and director of Titanic [CAM 97], staged the beauty and mystery of the deeps in a science fiction film, symmetrical of those dealing with space exploration in search of otherness. The Abyss is an adventure immersed in the infinite depths of the oceans and the human soul [CAM 89], perhaps illustrating these verses by French poet Charles Baudelaire (1821–1867): “The sea is your mirror; you contemplate your soul in the infinite unfolding of its blade – and your mind is no less bitter abyss!” (L’Homme et la Mer [BAU 57]). The oceans cover nearly 70% of the world’s surface and are the largest water reserve on our planet, accounting for 95% of the available volume. They also host the majority of living species on Earth [COS 15] – drawing up an inventory of them is a fundamental challenge for biodiversity knowledge: more than 90% of marine species are not yet fully described by scientists [MOR 11]. Contributing to the production of most of the oxygen we breathe, and accumulating carbon dioxide at the cost of acidifying their waters, the oceans generate many ecosystem services that allow humanity to live on the blue planet. Ocean modeling is a key tool for scientists to understand some of the mechanisms that are critical to the functioning of ocean ecosystems, the future of marine biodiversity and climate change. 4.3.1. Marine currents Their tremendous capacity to absorb CO2 or thermal energy makes the oceans the main regulator of climate. By mixing huge quantities of water, marine currents help to circulate the heat of our planet (Figure 4.9): a global flow whose

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mechanisms have been known for nearly a century, and whose importance on climate is nowadays the subject of many scientific studies.

Figure 4.9. The main currents of the North Atlantic (source: © IFREMER). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 4.9.– The map shows the main currents of the North Atlantic Ocean. Warm currents (red and orange) flow on the surface, moving up from southern areas to northern areas, whereas cold currents (blue) move deep in the opposite direction. Very cold and low-salt currents are measured in the boreal zones off Greenland and Canada (green on the map). While the North Atlantic is the largest engine of the “ocean conveyor belt”, other loops exist in other regions, such as the Pacific or the Indian. Carried away in these currents, a particle of water travels around the planet in a thousand years! The measurement campaigns at sea make it possible to understand the currents. France and the United Kingdom, with their partners, organize expeditions represented on the map by the black lines:

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between Portugal and Greenland (black spots) and between West Africa and Florida (black crosses). Different models make it possible to understand ocean dynamics, as Pascale Lherminier, researcher at IFREMER*, explains: “As close as possible to physics, ‘primitive’ equations (such as the Navier-Stokes equations) describe the dynamics of fluids and ocean currents. A simulation based on these equations is theoretically possible, but requires a very significant modeling and computational effort. ‘Theoretical’ equations may be deduced from the complete physical models: separating different effects, they constitute an ideal ocean model that makes it possible to understand each of them. ‘Large-scale’ equations reduce the size of models by filtering some of the information and physical phenomena. They allow simulations with a good compromise between computational cost and physical accuracy. This ‘equation-based’ modeling nowadays coexists with ‘data-based’ modeling. Data assimilation techniques allow, for example, to determine the conditions of a calculation by a means of a mathematical expression, while learning techniques make it possible to represent a physical process in the form of a ‘black box’, built from statistical observations.” These different models are used in ocean science, as in the other fields we cover in this book. The dynamics of the oceans remain very complex and data are still scarce, as scientists do not have as much information as for the atmosphere, for example. While satellites provide surface data, other systems (probes, floats) provide depth measurements (Figures 4.10 and 4.11).

Figure 4.10. Offshore measurement system (source: © P. Lherminier/IFREMER)

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“‘Argo’ is a program initiated in the 1990s to provide the international scientific community with ocean data. Nearly 4,000 floats are deployed in the oceans. Deriving freely, they collect information at depth, up to 2,000 or 4,000 meters today – the main part of the heat transfer phenomena occurring at a depth of about 2,000 meters. In addition, many countries are organizing measurement campaigns at sea, coordinated by an international program (Go-SHIP) to ensure better complementarity. With the OVIDE program, we carry out measurements every two years of different physical quantities characterizing the ocean: velocity, temperature, salinity, pressure, dissolved O2 and CO2, acidity, etc. Between the coasts of Portugal and Greenland, the ship carries out about 100 measurement profiles, from surface to bottom, at points about 40 kilometers apart.” The information collected is particularly useful for “reverse modeling”, which combines data to calculate physical quantities representing the state of the ocean from measurements [DAN 16, MER 15]. The transition from the second to the first is accomplished by means of “simplified equations”, which are established from the “primitive equations”. Inverse models allow to reconstruct an image of mass and heat transport on a depth profile, overcoming many technical difficulties: “On a hydrodynamic section, i.e. on a surface-to-bottom line, we calculate the current by vertical integration of the pressure anomalies. Filtering transient processes at small scales of time and space, the ‘integrated’ data is more reliable than the ‘averaged’ data, which can be parasitized by small fluctuations. One of the difficulties is that the integration process does not define a value in a unique way: additional information is needed. For example, it is possible to assume that the deep current is zero, but this assumption is not verified in practice. Missing information is obtained, for example, by measuring ocean elevation: surface data, provided by satellite observations, can be used to complete the current profile...” As some of the latest simulation results available show the variability of ocean currents (Figure 4.12), it is now up to scientists to interpret these results: “Ocean transport varies greatly from year to year and its 10-year variations are even greater! It remains to be understood whether this phenomenon is due to current climate changes or whether its causes are of a different nature. The existence of these cycles is not yet well fully explained...”

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While scientists, just like James Cameron’s film, find that the deep ocean retains many enigmas, the depths of their science are constantly filling up – and knowledge of marine currents is spreading in many areas (Box 4.1).

Figure 4.11. The international program “Argo” collects oceanological data through a network of nearly 4,000 floats spread throughout the world’s seas and oceans (source: www.commons.wikimedia.org). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Figure 4.12. Evolution of ocean transport relative to the North Atlantic “conveyor belt” between 1992 and 2016 (source: © IFREMER/CNRS/UBO). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMEN NT ON FIGURE E 4.12.– The figure fi shows the variations between 19922 and 2016 in volume flow in i the North Atlantic A from the tropics too the northernn seas fr models ffed by at the suurface, and inn the opposite direction at depth. Built from measureements at sea, the data show annual cyccles, with flow ws varying bettween 10 and 30 3 million m3 per p second, annd 10-year cyccles, with flow ws varying bettween 15 and 25 2 million m3 per p second. Thee Earth behavess like a giant maagnet, whose field is arranged around two poles close to the geographical poles p (Figure 4.13). 4 The Eartth’s magnetic field is predom minantly generated by the convection movem ments of the pllanet’s outer core, c which connsists of liquid metal m (mostly irron and nickel)). It in turn creaates electrical currents c that theemselves generate this field: the mechanism is thus t called “sellf-sustaining”. Present in a vast sppace around ouur planet, as welll as in its surfaace layers, the m magnetic field prrotects the planeet from chargedd particle curren nts: the solar wind. w Fluctuationns in the magnetic field affect different d system ms, causing disru uptions to teleccommunication systems (satellittes, submarine cables, etc.), degradation orr interruption of o satellite possitioning servicess, increased raddiation receivedd by astronautss and aircraft passengers, p or parasitic currentss in power gridss, which can caause power outaages over large areas! Undderstanding thee Earth’s magnnetic field in its smallest detaails allows scieentists to anticipaate these effectss while refiningg their predictio ons about the drift, d or even innversion, of the magnetic m poles – observed pheenomena that arre yet to be expllained! The oceeans also contribuute to the creeation of the Earth’s E magnetic field, althoough in much smaller proportions than the pllanet’s core.

Figurre 4.13. The Earth’s E magne etic field measured from spa ace (source: © ESA/ www w.esa.int). For a color version of this figure e, see www.iste.co o.uk/sigrist/sim mulation2.zip

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COMMEENT ON FIGURE 4.13.– The figgure represents the intensity of the Earth’s m magnetic field, measured m in Junne 2014 by the SWARM S probe launched by ESA. E It varies frrom 30 T (blue arrea) to 60 T (reed area). The Tesla T (T) is the unit of measurrement for the m magnetic field, naamed after the American physsicist of Serbia an origin, Nikollas Tesla (18566–1943), whose work w helped too understand annd exploit the electrical and magnetic propperties of matter. Marrine currents carry c the ions present p in seaw water and this circulation of charged particlees generates a magnetic m field. Satellite data enable scientissts to better unnderstand these phhenomena: launnched in 2013, three t satellites of the Europeann Space Agencyy as part of the SWARM S missioon, make it posssible to map th he Earth’s magnnetic field as a whole – and to identify i the partt attributable too marine currentts (Figure 4.14)).

Figurre 4.14. Image es of the magn netic field gene erated by ocean currents (ssource: https:://www.esa.intt/spaceinvideo os/Videos/201 18/04/Magneticc_tides). For a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip Thee data collectedd on this “magnnetic tide” also make it possibble to refine thee models used inn oceanology annd climatologyy. Knowledge of o marine curreents also contriibutes to understanding and antiicipating the evvolution of mariine pollution, pllastics or polym mers. Thee strength and malleability prroperties of theese materials haave made them m widely used inn many fields: health, h construcction, automotiive, aerospace, decoration, spports and packagiing. The masteery of polymeer dates back to the early 20th 2 Century w with the inventioon of Bakelite in 1907 by thee Belgian chem mist Leo Baeklaand (1863–19444). It has contribuuted to the deveelopment of thee packaging ind dustry: nowadaays, the vast maajority of the prodducts we consume are sold pacckaged. Bettween 1950 andd 2015, the totall production off plastics was esstimated at nearrly 8,300 tons. Note N that 70% of this materrial was used only once. Neearly 55% wass simply discardeed – the rest was incinerated or o recycled – an nd some of thiss material was found in the oceans (Figure 4.115). Containers of all sizes and d shapes, as weell as bags, invaded the world’ss seas and oceanns to the point of o forming a “seeventh continennt”.

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Figure 4.15. The e future of plasstics productio on in 2015 (sou urce: Our Worrld in Datta/https://ourw worldindata.org g/plastic-polluttion)

COMMEENT ON FIGURE 4.15.– In 20155, annual plastiics production represented r neaarly 270 million tons. Humans consumed 275 million in the same s year (inclluding productiion from previouus years). Nearrly 100 million were by the 2 billion people living less thaan 50 km away from fr the coast. Nearly 40 milllion tons of th his consumptionn was dumped into the environnment. Note thaat 8 million endded up in the seeas and oceanss, which carrieed nearly 10,000 and 100,000 toons of plastic onn the surface. Plasstic microdebriis floating on the t surface of the oceans aree ecological nuuisances, which can c lead to thee death of mariine species. Ing gested by fish, consumed by humans, micropllastics have the potential to be a public health h problem. In 2014, 2 environm mental researchhers conducted d a study to estimate the am mount of plastic drifting in the oceans and map m their distrib bution [SEB 155]. They estim mated the global amount a of micrroplastic particlles in the ocean ns to be betweeen 15 and 51 triillion (or billionss of billions) – representing a mass of 93,000 0,236,000 tons,, about 1% of tthe mass of plasttic waste dischaarged into the occeans in 2010. In order o to carry out the simulaations, the reseaarchers relied on o the largest ddatabase availablle to date, aggrregating the results of numerous flow measurement campaaigns, as has beeen the case worldwide w sincee the 1970s. Interpolation methods m well-knnown to scientissts allow in principle to map the dispersion of plastics froom the measureement of concenttrations in diffeerent areas (Figuure 4.16).

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Figure 4.16. Estimated number and mass of plastic microparticles in the oceans [SEB 15]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

As a remarkable feature of their study, the scientists chose to couple the concentration data with marine current models in order to estimate this dispersion with greater accuracy, and they also compared three different models to ensure the robustness of their calculations. Similar studies [SEB 12] have led their authors to develop an application for2 simulating waste dispersion in the oceans – and to popularize the notion of the seventh continent? Published at the end of the last century, the novel Le Roi des ordures takes as its backdrop this emblematic economic reality of our century [VAU 97]: that of the blatant inequalities produced by a system of production and consumption incapable of regulating its excesses. A fictional character, Don Rafael Gutierrez-Moreno, reigns as a ruthless godfather on Mexico City’s huge landfills where a crowd of poor people find their daily bread among the garbage. Waste is worth gold, and some chemical researchers know it. Damien Prim, researcher in catalytic science researcher at the University of Versailles Saint-Quentin, explains: 2 Available at: http://plasticadrift.org/.

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“Almost all the objects produced by our industry, from fertilizers to medicines and most everyday consumer goods, have been based for more than a century on the transformation of hydrocarbons. Replacing fossil resources with renewable resources requires technologies that still need to be developed and optimized... and it is our entire system of production and consumption of goods that must be reviewed – and eventually changed! We have about 20 years to accomplish it, if we want to organize new ways of producing.” The transformation processes used by fossil fuels are not operational for renewable raw materials: developing a bio-based chemistry that takes into account the entire design/recycling cycle is the subject of much current research. “The design must take into account the availability of the raw material and the energy cost of the transformations necessary to obtain a product... and this is not enough: valorizing, recycling and processing usefully and selectively is also fundamental. Giving the status of a discarded and/or unused object as a resource or waste raises ethical and legal questions. From the designer to the consumer, including the legislator, we are all concerned!” The emergence of new technologies, such as 3D printing (Figure 4.17), is, according to some, one of the challenges of the next century, as it could help recycle materials available in abundance in our waste [RIF 17].

Figure 4.17. “From mass production to mass production”: 3D printing to recycle a material as abundant as plastic? (source: www.123rf.com) Box 4.1. Using models and current data

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4.3.2. Climate What about the climate? In contrast with the weather forecast, which is concerned with changes in the “very short-term” (hours or days) of the atmosphere and oceans in various location, climate study focus on long-term variations (occurring in decades, centuries or even millions of years). Understanding and predicting the likely evolution of Earth climate is a current scientific challenge to which modeling contributes. Variations in the states of the atmosphere and oceans are the result of a large number of phenomena that can be represented numerically. A climate model may therefore be based on the coupling between the dynamics of the atmosphere, with the models mentioned above, and that of the oceans. The equations of fluid mechanics are present behind the simulations. They are complemented by various other factors, which describe the variety of interactions in the climate system: – interactions between chemical species in the atmosphere (some resulting from human or plant activities, such as carbon dioxide, methane or ozone emissions) and energy transfers by radiation, emitted or absorbed as a result of the presence of these chemical species; – interactions between the continental biosphere (photosynthesis, respiration, plant evapo-transpiration) and the atmosphere; – interactions between ocean bio-geochemistry (plankton, carbon compounds, etc.), the carbon cycle in the global climate system and ocean circulation; – interactions between sea ice (model of the same type as the ocean or atmosphere model), the ocean and the atmosphere, or between continental ice, land and the atmosphere. In addition, “radiation forcing” describes the amount of energy received by the Earth’s atmosphere from solar radiation and is a key element in climate simulations, whose ability to account for such complex interactions improved over decades. The models used today for climate studies compiled and assessed by the Intergovernmental Panel on Climate Change (IPCC)3 integrate all possible phenomena (Figure 4.18). 3 The IPCC is an intergovernmental body of the United Nations aimed at providing the world with a scientific view of climate change. It does not carry out original research (nor does it monitor climate or related phenomena itself), but it assesses published literature on the subject. IPCC reports cover the “scientific, technical and socio-economic information relevant to understanding the scientific basis of risk of human-induced climate change, its potential impacts and options for adaptation and mitigation” (see, for instance, https://www.ipcc.ch). IPCC reports may serve as ground for the elaboration of public policies – and, to some citizens, for individual action.

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Figure 4.18. The complexity of climate prediction models has increased in recent decades [TRE 07]

COMMENT ON FIGURE 4.18.– The figure shows the evolution of modeling assumptions in climate studies from the 1970s to the present. Relatively simple in origin, the models take into account solar radiation, precipitation and CO2 emissions into the atmosphere. Climate models are becoming richer and gradually integrating other effects. First, the influence of clouds in the atmosphere and glaciers in the oceans, then all known phenomena: volcanic activity, the complete carbon and water cycle, emissions of other gaseous substances and aerosols, as well as the chemical reactions they undergo in the atmosphere. FAR, SAR, TAR and AR4 refer to the first four reports published in 1990, 1995, 2001 and 2007. The fifth report was released in 2014, and the latest report was published in 2018 (source: https://www.ipcc.ch/publications_and_data/publications_and_data_reports.shtml) Ocean modeling represents the dynamics of marine currents, rendered by fluid mechanics equations. This is influenced by salinity effects, ice or marine vegetation in some ocean regions. Atmosphere and oceans evolve simultaneously. Wind and heat exchange influence the sea surface state, while ocean temperature is transmitted to the atmosphere. Simulations account for these mechanisms by coupling calculation tools specific to the digital representation of the atmosphere and the ocean. Before each calculation, the initial state of the oceans is determined by data assimilation methods. The data for wave height, temperature, salinity, etc. come from observations and measurements at sea. They make it possible to force the physical model to take as the initial condition of the calculation the state closest to

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that observed, in order to give the greatest possible accuracy to the simulations. The equations will then do the rest to represent the evolutions of the ocean. The resolution of the simulations has constantly been refined (Figure 4.19). In particular, some calculations use the most efficient computational means at disposal – such as high performance computing (Chapter 3 of the first volume) – making it possible to study many scenarios. Gérald Desroziers, research engineer at MétéoFrance, explains: “A simulation is nowadays typically based on 10 million calculation points, arranged with a resolution of 50 to 100 kilometers. This resolution is imperative when it comes to representing the atmosphere and oceans globally! One month of computation time makes it possible to produce data from about 10 scenarios of evolution over 100 years: these computation times are perfectly acceptable for research studies.”

Figure 4.19. The geographical resolution of successive generations of climate models has steadily increased [TRE 07]

COMMENT ON FIGURE 4.19.– The figure represents the successive generations of models used by scientists studying climate change by the means of simulations: it shows how their resolution has increased, taking the example of Northern Europe. The mesh size has typically increased from 500 to 110 km between 1990 and 2007. The latest generation of numerical models have the highest resolution and they are adopted for simulations of short-term climate change, i.e. over several decades. For long-term evolutions, simulations are conducted using the model of the previous

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generation in order to reduce calculation times. Vertical resolution is not represented, but has evolved in the same proportions as horizontal resolution: studies reported the first IPCC report used one ocean layer and 10 atmospheric layers to reach 30 atmospheric and oceanic layers in the latest generation of models. FAR, SA, TAR and AR4 refer to the four successive climate reports published by the IPCC in 1990, 10997, 2001 and 2007, respectively. With different scenarios, on average between 50 and 100 are needed, scientists have access to statistical data to study the influence of different model parameters (e.g. moisture content and concentration of a chemical species) on possible climate states. As with weather forecasting, this approach makes it possible to accompany the calculations with a reliability estimate, which is essential to propose scenarios that may realistically contribute to anticipating climate change. Simulations can be used, for example, to model a probabilistic ocean. Based on different hypotheses, they provide access to mean ocean states and estimate the variability of the physical quantities that characterize them. Calculations allow the reproduction of the past evolution are of state of the oceans and can represent its variability over time (Figure 4.20).

(a) Mean temperature

(b) Temperature variability Figure 4.20. Calculation of ocean surface temperature. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 4.20.– The figures represent the numerical simulation results of the ocean surface temperature. Calculations are made using the OCCIPUT (Computing platform for volumetric imaging) code, developed at CERFACS (European Center for Research and Advanced Training in Scientific Computing). The first figure represents the surface temperature of the oceans in degree Celsius on October 1, 1987. The daily average temperature obtained by simulation is between 0°C (black and blue areas) and 30°C (red and white areas). The second figure represents the intrinsic variability of this temperature on December 31, 2012. This is a 5-day average calculated using 50 simulations over 45 years of observation. The variability is between 0–0.2°C (in black and blue) and 0.8–1°C (in red and white) [BES 17, LER 18, SER 17a]. In France, CERFACS* works in collaboration with Météo-France to conduct climate simulations that contribute to IPCC reports. The data from the simulations are compared with measurements and attest to the validity of the models. Their reliability to predict possible ocean and climate changes is established (Figure 4.21), as Olivier Thual, a researcher at CERFACS, explains: “Models are nowadays able to accurately represent past climate changes. They help to predict its variability in a way that is quite convincing to the scientific community. Simulation has become a major tool of interest in climate change studies.”

Figure 4.21. Contributing to the study of climate, numerical modeling is used to understand the influence of human activities on the global temperature evolution observed in the 20th Century [MEE 04] For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 4.21.– A set of numerical simulations conducted in 2003 using global models allows to study the influence of various known factors on climate

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change. Two of them are of natural origin (solar radiation and volcanic emissions), the others correspond to certain human activities (including emissions of various aerosols and greenhouse gases). The simulations are compared with available temperature data: the calculations highlight the influence of factors attributable to human activities – and explain the temperature increase observed since the 1960s. Modeling, whose finesse has increased since 2003 (Figures 4.16 and 4.17), contributes to the development of the various climate change scenarios, as presented in IPCC reports. The figure shows the evolution of the difference between the mean global temperature and its observed value over the period 1890–1919. This evolution is measured and simulated over the period 1890–2000. The global average value is an indicator that does not reflect local variations. However, similar trends have also been confirmed for temperature evolutions in various regions of the world. These conclusions have been challenged by some scientists, who think that models fail to fully understand or explain meteorological phenomena and cannot reliably justify them [LER 05]. Science in general is an ongoing process that proceeds through discussion and interpretation of scientific results to reach consensus. To this day, the scientific community largely agrees on these conclusions elaborated with the knowledge available. Climate change continues to be positioned at the core of numerous researches, some using both observation data and simulation results, in order to further improve understanding and refine predictions. As emphasized above, climate changes depend, among other things, on the amount of energy brought into the atmosphere and oceans from two main sources: electromagnetic radiation from the Sun and thermal radiation from the Earth itself. The presence of clouds in the atmosphere influences these mechanisms explains Blandine L’Hévéder: “Clouds reflect solar radiation back to space, thus decreasing the solar energy absorbed by the atmosphere, which tends to cool it down: this is the ‘albedo’ effect. On the other hand, they form a shield against the Earth’s thermal emission, isolating the surface that loses less heat, which this time tends to warm the atmosphere: it is the ‘greenhouse effect’. These two opposite effects tend to compensate each other, but depending on the type of cloud, one of them prevails over the other. High clouds (cirrus, cirrostratus and cirrocumulus) have a significant greenhouse effect and tend to warm the atmosphere, while low and medium clouds (stratocumulus, cumulus, nimbostratus) have a strong albedo effect and tend to cool the atmosphere.” Modeling the presence and influence of clouds in the atmosphere is therefore crucial to represent the greenhouse and albedo effects as accurately as possible. The current limitations of cloud modeling and their response to climate change explain much of the uncertainty in predicting global temperatures and climate impacts summarized in the IPCC scenarios:

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“Global climate models solve the movements and thermodynamics of the atmosphere at the 10-kilometer scale, while turbulent air movements, responsible for cloud formation and maintenance, occur at a much smaller scale (in the order of 10 meters or less). In order to take into account phenomena that they ignore, global climate models incorporate equations that empirically link the occurrence of clouds to large-scale calculated variables, such as temperature or humidity. However, such modeling does not provide sufficiently accurate estimates of cloud cover.” The joint development of new, more accurate calculation methods and new, faster calculation methods allows scientists to refine models: “One of the solutions proposed to understand and represent cloud dynamics and thermodynamics is to use LES (Large Eddy Simulation) models to solve the equations of turbulent motion in clouds at the scale of 10 meters. This makes it possible to explicitly simulate the interaction between clouds and turbulence.” This approach is being used by researchers to study the influence of stratocumulus in global warming [SCH 19]. These low clouds cover about 20% of the ocean surface in the world’s temperate zones. They are particularly found in the eastern parts of the oceans, for example along California, Mexico and Peru. As they do not contain much water, they precipitate little and persist for a long time in the atmosphere. Being at low altitude, their temperature is close to the Earth’s temperature and their greenhouse effect remains limited. On the other hand, their reflectivity is in the order of 40–50%: it contrasts very strongly with the reflectivity of the ocean, which is much lower (5–10%). Stratocumulus therefore have a strong albedo effect and, by regulating air temperature, they play an important role in the thermal balance of the climate.

Figure 4.22. Atmospheric simulations with cloud modeling (source: Kyle Pressel, California Institute of Technology)

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COMMENT ON FIGURE 4.22.– The figure shows a simulation result of LES (Large Eddy Simulation) performed on an atmosphere model. The calculation accounts for the formation of tropical cumulus clouds (here in the Barbados region), which global climate models are not able to achieve. This type of modeling makes it possible to more accurately represent the influence of clouds on climate. However, due to their calculation cost, simulations are still limited to local studies. “Using LES models, the researchers carried out various simulations by varying the concentration of CO2 in the atmosphere. A reference simulation, assuming a fixed rate of atmospheric carbon dioxide (400 ppm, its current concentration), correctly reproduces the observed cloud cover. A new simulation allows to evaluate the consequences of an increase in the CO2 rate from 400 to 1,600 ppm. The results of the LES calculation first highlight the same effect as predicted by the global models: an increase in CO2 content leads to an increase in sea surface temperature, with the cloud cover remaining dense, while the amount of liquid water in the clouds decreases. Calculations also reveal that when a concentration threshold is exceeded (above 1,200 ppm), stratocumulus coverage becomes unstable and disintegrates into scattered clouds. A phenomenon that cannot be predicted by global models, which are insufficiently precise...” The lessons that researchers are learning from these more precise models are many: “Because of the disappearance of the cloud layer and its albedo effect, the solar energy absorbed by the ocean surface increases. This leads to a local temperature increase of 10°C. In order to reform cloud-cover similar to the original one, calculations indicate that it is necessary to descend to CO2 concentrations much lower than those at which instability was triggered, i.e. below 300 ppm (the concentration level found in the 1950s)”. This type of modeling may illustrate that climate dynamics is highly “nonlinear” [GHI 07] and that it is currently in an unstable equilibrium state: one of the possible evolution scenarios is that of a shift to a state where the cloud cover of the ocean would be fundamentally modified. For the time being, calculations are being carried out on a small area of the ocean, under large-scale conditions representative of summer in subtropical regions – a specific case that does not allow general conclusions to be drawn. Additional studies may confirm or refute this scenario and possibly assess its consequences on climate: they may be carried out through finer modeling, while they gradually become accessible to climate scientists. Box 4.2. Modeling the influence of clouds more accurately

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Clim mate simulationns are based on o a wide variety of modelinng: the resultss of about 30 climaate models deeveloped arouund the world d are analyzeed in IPCC reeports, as Blandinee L’Hévéder explains: e “Thhis diversity of models is i essential for f assessingg the uncertaainty associated with climate moddeling. In a set s of calculaation results, the nto two subsett of equal weiight. median value off the results diivides them in d set prodduced by clim mate Sciientists assertt that the meedian of the data models is a relevvant value: prroviding estim mates close to the measurem ment orical climate simulations.” data, it attests to the overall vaalidity of histo It is partly thankss to scientificc computation n that the reccommendationns of the ferent scenarioos they prodduce give IPCC exxperts are coonstructed – and the diffe indicatioons on the shhare of climatte change maay be influencced by humann activity (Figure 4.23). 4

Fig gure 4.23. Possible evolutio on of the Earth h’s temperaturre under differrent greenhouse gas emission assumptions

COMMEN NT ON FIGURE E 4.23.– The figure f shows different d scenarios for the evolution of the gllobal average temperature by 2100 undeer different greeenhouse gas emission policies. Greenhouse gas emissionns are measurred in tons off CO2 equivallent. “No p thee scenario evvaluates the evolution e of em missions if noo climate climate policies”: policy iss implementedd; it concludess that there is a probable inncrease in tem mperature between 4.1 and 4.8°C by 21000, taking as a an initial situation thhe global temperattures observeed before the industrial erra. “Current climate policcies”: the scenarioo forecasts a warming w from m 3.1 to 3.7°C C by 2100, baased on curreent global policies. “National pledges”: if alll countries meet m their greeenhouse gas emission

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reduction targets as defined under the Paris Agreement, it is estimated that global warming will range from 2.6 to 3.2°C by 2100. The Paris Agreement, signed in 2016, sets a target of 2°C. “2°C Pathways” and “1.5° pathways”: these two scenarios show the effort required to limit warming to 2°C and 1.5°C, limits considered acceptable by many scientists in order to avoid significant changes on our living conditions on Earth. Scenarios for increasing global temperature below 2°C require rapid reductions in greenhouse gas emissions: in a context where energy is a major contributor to greenhouse gas emissions, the task for humanity seems very ambitious (source: OurWorldinData/www.ourworldindata.org). The consequences of climate change are potentially universal and widespread – economy, security, infrastructure, agriculture, health and energy [MOR 18]. Anticipating them and equipping humanity with the technical, legal and political means to adapt to them is undoubtedly one of the essential challenges we face at the beginning of the 21st Century. While, from China to the United States, via Europe, humanity once again imagines projecting itself into space in order to reach Mars or exploit the resources of the Moon [DEV 19, DUN 18, PRI 19], atmospheric and climate modeling, as well as the message from astronauts who have experimented with the Overview Effect (Figure 4.24), may remind everyone that our destiny is, at least in the short term, terrestrial – that is, essentially, oceanic.

Figure 4.24. Blue Marble: Earth photographed from space during the Apollo 17 mission on December 7, 1972 (source: ©NASA)

5 Energies

Cinema was born at the end of the 19th Century; it was innovations in optics, mechanics and chemistry that made possible the development of photosensitive supports and mechanisms that, because of retinal persistence, synthesize movement. Some of the research preceding its invention had an essentially scientific purpose. At that time, the English photographer Eadweard James Muybridge, like the French native Etienne-Jules Marey, was interested in movement. Marey’s pictures show that during a gallop, for example, the horse does not have all four legs in the air! In 1878, Muybridge arranged a series of cameras along a racecourse. Triggered by the horse’s passage, the shots separated the movement (Figure 1.29 in the first volume) then allow an animated sequence to be obtained. His experience preceded the invention of the American engineer Thomas Edison (1847–1931): in 1891, the kinetograph was the first camera to be used. In France, inventors Auguste and Louis Lumière (1862–1954 and 1864–1948) filed the cinematographer’s patent in 1895 – both a camera and an image projection camera, it was invented before them by Léon Bouly (1872–1932). The Lumière brothers shot a series of films with their camera and offered private screenings. The story of the first showing of the Arrivée d’un train à La Ciotat [LUM 85] recounts that the animated image of the train seeming to burst through the screen towards the audience sent them screaming and rushing to the back of the room. 5.1. The technical dream The development of steam locomotives is also a symbol of the technical control of movement, made possible by thermodynamics and mechanics. In the early 19th Century, the United Kingdom saw the birth of these new machines and inaugurated the first railway line in 1812. The Middleton Railways received the Salamanca

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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(Figure 5.1), built by British engineers Matthew Murray (1765–1826) and John Blenkinsop (1783–1831), it was the first commercially operated steam locomotive.

Figure 5.1. The Salamanca (1812) – schema first published in The Mechanic’s Magazine in 1829 (source: www.commons.wikimedia.org)

COMMENT ON FIGURE 5.1.– Power refers to the ability of a device or system (mechanical, chemical, biological, etc.) to deliver a given amount of energy in a given time. Before the advent of steam engines, humans often drew the energy necessary for hitch traction from horses. The English physicist James Watt (1736– 1819) proposed horsepower as a unit of power measurement. Watt uses as a reference the power required to pull 180 pounds (or 0.4536 kg) of weight at a speed of 3.0555 feet per second (or 0.93 m/s) to overcome gravity (9.81 m/s2). The corresponding power is the product of this mass, speed and acceleration, approximately 745 W (the power unit being named in his honor). The French physicist and engineer Nicolas-Léonard Sadi Carnot (1796–1832) contributed to the development of thermodynamics, the science of heat. In 1824, he published a book acknowledged as being a major contribution to physics: Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. Thermodynamics gave the framework for studying the functioning of thermal machines and designing them. The Industrial Revolution marked the advent of machines and the growing importance they occupy in human life. They even became protagonists in their fiction, like The General, led by Johnnie, the character incarnated by American actor Buster Keaton (1895–1966) in his 1926 film. The machine is his second love, and when Annabelle Lee, his fiancée, is kidnapped by a squadron of the northern armies, it is with the help of the locomotive that he starts a steam chase race to save her [KEA 26]!

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Large-scale access to mechaniccal energy haas given hum manity a new power to a shape the world by pusshing the limitts of its physiical constraintts. French control and engineerr Jean-Marc Jaancovivi summ marizes the history of the industrial i revoolution as follows: machines) po owered by a super-powerfful “[It] is the innvention of (m w how to exploit directly [....] ennergy that thee human body does not know Itt has allowedd us to overtuurn in two centuries c the multi-millenaary hierarchy betw ween environm mental constraaints and our desires [...] W We b of thee world on ou ur desires: it is the techniccal have set the borders N 18]. drream...” [JAN Realiizing this dreaam, still restriicted nowaday ys to the richhest humans, rrequires a large am mount of enerrgy, the consttant increase in i which raisses the questioon of the possible exhaustion of o available reesources for humanity h (Figgure 5.2). This energy consumpption also exploits carbonacceous sources, which are paartly responsibble, along with othher human activities, a forr the emissio on of many compounds into the environm ment.

Figure 5.2. 5 Evolution of world energ rgy consumptio on between 1965 and 2016 6 (source: Our Wo orld in Data a/ https://ourrworldindata.o org/energy-pro oduction-and-cchangingenergy-ssources) For a color verrsion of this figure, see www.iste.co.uk/sigrist/ simulatio on2.zip.

COMMEN NT ON FIGURE E 5.2.– In 1965 5, world energ gy consumptioon was just oveer 40,000 TWh, and it was just over o 145,000 TWh T in 2016. In the same year, y it breakss down by c 50,000 TWh T for oil, 400,000 TWh forr gas; the origin ass follows: 40,0000 TWh for coal, 15,000 TWh T are brokeen down into hydraulic (ab bout 5,000 TW Wh) and nucleaar (about

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3,000 TWh) electricity and renewable energy sources (about 2,000 TWh). In 2016, more than 90% of the energy consumed by humans came from hydrocarbon combustion and 2% from renewable sources. 1 TWh refers to a thousand billion Watts per hour (unit of energy consumption). 1 TWh corresponds, for example, to the energy consumed by 10 billion people using a standard laptop computer for 2 h. The energy sector, strategically contributing to the future of humans, makes extensive use of numerical simulation in order to: – optimize the operation of energy production machines; – demonstrate the expected safety and security requirements of sensitive installations; – research new energy production processes. This chapter provides examples of these in different areas of the energy sector. 5.2. Combustion In 1865, Jules Verne published From Earth to the Moon. The novel imagines the combination of different “technical bricks” (propulsion, aerodynamics, metallurgy, etc.) in order to realize the dream of conquering space [VER 65]. The writer also questions the motivations of humans and their relationship to technology. In this fictional world, it is partly the boredom, caused by the absence of conflict, which diverts the passion for the weapons of the Gun Club members toward the design of a super projectile, propelled to conquer the Moon. Verne thus anticipates more than half a century of history: “They had no other ambition than to take possession of this piece of the continent from the air and to fly at its highest summit the starry flag of the United States of America” [VER 65]. Imagined by the French director Georges Méliès (1861–1938) [MEL 02] or the Belgian draftsman Georges Rémi (1907–1983) [HER 53, HER 54], the first steps of humans on the Moon became a reality when the American astronaut Neil Armstrong (1930–2012) took them on July 21, 1969, leaving his mark on the sea of tranquility [CHA 18]. The heroes of Verne and Méliès join the Selene star aboard a giant revolver ball pulled out of the earth’s gravity propelled by an immense cannon; in Hergé's comic strip, Tintin and his companions achieve their objective because of the atomic rocket imagined by Professor Tournesol. However, the 20th Century space conquest was achieved by means of combustion engines – propulsion based on the ejection of gas at high speed through a nozzle behind the launchers.

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The take-off t phasee is one of thee most critical: in order to optimize o the deesign and improve the perform mance and robbustness of launchers, l enggineers offer multiple s is a tool thatt helps now wadays to technical solutions. Numerical simulation a guide deesign choices (Figure 5.3). Thierry understaand complex phenomena and Poinsot, a researcher in combustioon simulation,, points out thhat simulationns of this type requuire significannt resources: “A A simulation like that of thhe Ariane V ro ocket engine represents r aboout 1,500 years onn a computer equipped e with h a single processor! The uuse of supercompuuters makes it possible to make theese simulatioons acccessible in onnly three weekks of calculatiion”. Intennsive exploitaation of hydroocarbons (gass, oil and coaal), pollution of urban areas, grreenhouse gass emissions: combustion c is a mechanicall and chemicaal activity with mulltiple consequuences on our environment. The most vissible are waterr vapor or smoke emissions e thaat modify landscapes and ecosystems. Behind the bbeauty of industriaal flows obserrved at certaiin times of th he day (Figurre 5.4) are soometimes irreversibble changes in the enviroonment, to which w our lifeestyles contribbute very significaantly.

Figure 5.3. Back body b calculatio on for Ariane V (source: ©ONERA). O For a color version of this t figure, see e www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGURE E 5.3.– The ca alculation pressented is baseed on the aeroodynamic code “E Elsa”, developped in Francce by ONERA A. The flow of o propulsion gases is

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turbulent and compressible, at Mach 0.8, so close to the speed of sound. This involves using calculation methods that account for both effects, which is a complex task. The proposed simulation, based on a modeling of the large scales of turbulence, requires nearly 120 million calculation points! It highlights the origin of the influence of the asymmetric fasteners of the boosters to the central body on the flow dynamics and lateral forces exerted on the launcher. A fine simulation requiring dedicated resources and skills, it produces valuable results for designers. More generally, combustion indirectly affects the living conditions of billions of people in both industrialized countries and large emerging economies, which invest massively in this area. Today, 85% of the energy produced in the world comes from the combustion of hydrocarbons (Figure 5.2). An observation made by the American photographer Alex MacLean, for example, with a series of photographs taken, among others, above industrial production sites, mining sites, etc. [MAC 08]. Combustion-engine-powered machines, and a large part of industrial activity, still contribute to meeting various human needs: food, heating, mobility. In a context where this trend has not yet been largely reversed in favor of alternative energy production methods, numerical simulation is being used to design more efficient and less polluting engines, as well as to test the efficiency of new resources, such as biofuels.

Figure 5.4. Smoke and steam rising above an industrial complex (source: www.123rf.com/Shao-Chun Wang)

COMMENT ON FIGURE 5.4.– Thermodynamics, the science of heat, is based on two main principles. The first stipulates that the total energy of an isolated system is always conserved – and therefore remains constant (energy conservation principle). Energy cannot therefore be produced “ex nihilo” and can only be transmitted from one system to another: in other words, “one does not create energy, one transforms it”. The second establishes the “irreversibility” of physical phenomena, particularly during heat exchanges (thus thermal energy is spontaneously transferred from the

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hot body to the cold body). The second principle postulates the existence of a physical function, “entropy”, expressing the principle of energy degradation or characterizing the degree of disorganization, or unpredictability of the information content of a system. The second principle stipulates that the entropy variation of a system is always positive: energy “production” is therefore always accompanied by heat losses, waste production, etc. Thus, the second principle also serves to calculate the efficiency of a machine, an engine, a nuclear plant, a wind turbine, etc. It also indicates that there is no such thing as “renewable energy”, even if it is possible to produce energy from abundant sources (sun, wind, tides, etc.). Note that here we use, by extension of language, the term “energy production” to designate what physicians describe as “energy transformations”. Combustion involves liquid or gaseous chemical compounds that flow and are burned in the thermal chambers of engines. The simulations are thus based on the equations of fluid mechanics, coupled with those of chemical reactions: “Hundreds of different species and thousands of chemical reactions occur during combustion. This is the case, for example, for traditional fuels (kerosene, petrol) and bio-fuels, whose energy and chemical properties are to be assessed by calculation. The challenge of simulation is reporting on it. The latter has three major difficulties: the geometries studied are complex, the flows involved are highly turbulent and the kinetics of chemical reactions require highly accurate models”. Chemical reactions occur in extremely short times, in the order of one nanosecond, or one billionth of a second (the equivalent of a day over a period of 1 million years). The simulation aims to represent them by calculating their evolution over time, the way they mix and are transported in the flow, which is also marked by turbulent phenomena, the latter thus being modeled as accurately as possible. For example, the ignition sequence of a gas turbine is a critical phase, usually not studied by engineers by means of a calculation, due to its complexity. A full simulation was conducted by researchers in 2008 on one of the world’s leading supercomputers in the United States (Figure 5.5). It represents the actual geometry of the turbine, composed of 18 burners lit successively. It allows the study of the propagation of the ignition flame around the turbine perimeter. Turbulence is represented down to small vortex scales. The calculation requires tens of millions of CPU hours to simulate phenomena that actually occur in tens of milliseconds. Optimizing the propulsive performance of an engine by limiting undesirable pollution effects requires a large number of simulations, the unit calculation cost of which is significant since the calculation models contain several hundred thousand unknowns.

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Research and development in this field is a major strategic challenge: it involves many scientists in Europe, the United States and India or China, a country that invests heavily in the training of its engineers and equips itself with highperformance computing machines (Chpater 3 of the first volume). Maintaining the correct level of combustion calculation codes is, as with other tools, a major task. The latter employs several dozen full-time engineers and researchers in the various R&D* centers interested in this theme. For them, it is a question of adapting the code to the thousands of processors of computing machines that are and will be used, for example, by manufacturers. “Designing turbines only with simulation is however not an option these days: the stakes of reliability, robustness and propulsion performance are too high to do without one-scale prototypes. But simulation also complements the tests and thus helps to reduce design costs”.

Figure 5.5. Simulation of a gas turbine ignition sequence [BOI 08]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 5.5.– The figure shows the gas state calculated in the body of a turbine 45 milliseconds after ignition. The initiation points of the sequence are indicated in red (top left and bottom right). The data shown are the gas velocities in the turbine axis (scale ranging from −20 m/s in light blue to +20 m/s in yellow), with the fastest gas temperatures superimposed (scale ranging from 273 K in turquoise to 2,400 K in red) and the flame front progression zone (bright light blue), corresponding to the maximum mass flow.

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5.3. Nuclear energy Some scientific discoveries are made by chance or by error, as is the case with radioactivity. In the late 19th Century, the German physicist Wilhelm Rögten (1845–1923) became passionate about cathode rays, generated by means of “Crooke tubes” – the ancestor of the tubes of the first television sets. With this device, he discovers a type of radiation capable of penetrating into matter (Figure 5.6): he designates these rays as the letter X, symbol of the unknown.

Figure 5.6. X-ray of the bones of a hand with a ring on one finger, Wilhelm Konrad von Röntgen, 1895 (source: Wellcome Collection/www.wellcomecollection.org)

COMMENT ON FIGURE 5.6.– On December 22, 1895, Wilhelm Röntgen made the first X-ray photograph in history by inserting his wife Anna Bertha’s hand between a Crookes tube and a photographic plate. He notes that “if you put your hand between the discharge device and [a] screen, you see the darker shadow of the bones of the hand in the slightly less dark silhouette of the hand”. The densest and thickest parts are the darkest on the plate: you can see a ring on the ring finger. Radiography was born! It is now widely used as an imaging medium in the medical field or in materials science – where it is part of non-destructive testing (Chapter 2). 5.3.1. Dual-use energy The discovery of Rögten, presented in January 1896 at the Paris Academy of Sciences, intrigued the French physicist Henri Becquerel (1852–1908), who was, at

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the same time, interested in the phenomenon of fluorescence. In order to understand it, he worked with phosphorescent uranium salts deposited on photographic plates: exposed to the sun outdoors and later developed, they reveal the image of salt crystals. Becquerel attributed this phenomenon to Röntgen’s rays: he believed that solar energy is absorbed by uranium salt before being re-emitted in the form of Xrays, which then impresses the photographic plates. On February 27 the same year, while trying to expose his photographic plates, the weather was unfavorable to him: disappointed to see the sunlight stubbornly hidden behind the clouds, Becquerel put plates already impregnated with uranium salt in a cupboard, hoping for better conditions for a new experience. A few days later, on March 1, he still developed these plates and discovered that they were still impressed. The phenomenon was that of a spontaneous emission of radiation by uranium: Becquerel had just discovered radioactivity1. French scientists Marie and Pierre Curie (1867–1934 and 1859–1906) followed Becquerel in their search for new “radioactive” substances, according to the terminology they had proposed. In 1898, they discovered Radium and Polonium. They suggested that radioactivity is an atomic phenomenon. “Something is happening inside the atom”: their insight disrupted the atomic theory inherited from Greek antiquity, according to which the atom is thought of as unbreakable. In 1934, the French physicists Irene Curie (1897–1956) and Frederic Julliot (1900–1958) paved the way for artificial radioactivity by synthesizing a radioactive isotope of Phosphorus that does not exist in nature. Following Irene Curie’s work, German chemists Otto Hahn (1879–1968) and Fritz Strassman (1902–1980) discovered in 1938 that uranium bombarded by neutrons gave rise to two lighter elements. Nuclear fission is thus understood on the eve of the Second World War. In the context of this conflict, this discovery led to the development of weapons with unparalleled destructive power (Chpater 3 of the first volume). After 1945, nuclear energy was used in power plants: the first nuclear power plant was built in the United States in 1951, soon joined in the development of this technology by the Soviet Union (1954), Great Britain and France (1956) – these countries also acquiring nuclear weapons. After experiencing significant development between the 1960s and 1980s, the nuclear industry, one of the most regulated, also became one of the most controversial. The shock caused by the disasters of Chernobyl in 1986 and

1 X-rays are emitted during electronic transitions, the passage from one energy level to another by an electron. Becquerel discovered gamma rays, resulting from the disintegration of atoms, which were explained in 1919 by the English physicist Ernest Rutherford (1871– 1937). X and gamma rays are two electromagnetic waves, emitted at different frequencies (Figure 2.15 of the first volume).

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Fukushim ma in 2011, and a the manaagement of haazardous wastte it generatess, has led the citizeens of some Western W countrries to want nu uclear energy to be phased out. In 20015, the Inteernational Atoomic Energy Agency (IAE EA), the inteernational observerr body on nucclear energy and a its civil or o military appplications, reccords 435 nuclear reactors r in serrvice worldwiide. The majo ority are basedd on PWR (prressurized water reeactors) and are a located in the United States, S Francee and Russia (after the Japanesee reactors werre shut down)). The IAEA also a estimatess that by 20500, nuclear power will w account foor 17% of gloobal electricitty production.. This increasse will be particulaarly relevant inn developing countries, acccording to thee IAEA: 68 reaactors are under coonstruction inn 15 countries,, including 25 5 in China [SFE 16]. As aan energy source claimed to be low in CO2 em missions2, nucclear power iss, for some, oone of the uction in the 21st 2 Century. answers to the challennges related too energy produ The future f of nucllear energy may m be that of fusion, whichh experimentaal reactors nowadayys aim to conntrol. Whetherr based on on ne or the other of these teechniques (Figure 5.7), nuclear energy contrrol is partly based on num merical simullation, of w will give soome examples of its use. which we

Figure 5.7. Nuclear energy e is obta ained by fission n or fusion: if the t former is a proven hnique, the lattter remains to o be invented (source: ( www..shutterstock.ccom) tech

It shhould be noteed that in Frrance, there are many sim mulation tools whose developm ment has beeen driven byy the needs of o the nucleaar industry. B Based on 2 In factt, no mode of energy producction really is,, when taking into account eextraction, transform mation and of prrimary sources (hydrocarbons,, uranium), buillding and mainntenance of productioon sites (refineryy, power plant), waste manageement, etc.

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knowledge and innovations, largely funded by the community, not all of these tools have been commercially oriented and remain accessible to a broad global scientific community today. 5.3.2. At the heart of nuclear fission A nuclear power plant produces electricity from the heat released by the decay of a heavy atom (formed by a large number of nucleons, such as uranium, plutonium, etc.), under the action of a neutron (Figure 5.8).

Figure 5.8. Nuclear fission (source: www.shutterstock.com). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 5.8.– Uranium is an element composed of heavy atoms. These atoms have a nucleus that can break into two smaller nuclei under the impact of a neutron. Since the neutron has no electrical charge, it can easily approach the nucleus and penetrate inside without being pushed back. Fission is accompanied by a large release of energy and, at the same time, the release of two or three neutrons. The released neutrons can in turn break other nuclei, release energy and release other neutrons, and so on, causing a chain reaction (source: www.edf.fr). In nuclear reactors, the chain reaction is controlled by devices made of materials that can absorb neutrons. It is therefore possible to vary the power of a reactor to produce electrical energy (Figure 5.9).

Figure 5.9. Schematic diagram of the operation of a nuclear power plant (source: www.123rf.com/Fouad Saad). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 5.9.– In PWR reactors (Pressurized Water Reactors, currently operating in France for example), the heat produced by the fission of uranium atoms increases the temperature of the water flowing around the reactor. The latter is kept under pressure to prevent the reactor from boiling. This closed circuit, called the primary circuit, exchanges energy with a second closed circuit, called the secondary circuit, through a steam generator. In the steam generator, the hot water in the primary circuit heats the water in the secondary circuit, which is transformed into steam. The pressure of this steam turns a turbine, which in turn drives an alternator. Thanks to the energy supplied by the turbine, the alternator produces an alternating electric current. A transformer raises the voltage of the electrical current produced by the alternator so that it can be more easily transported in very high voltage lines. At the outlet of the turbine, the steam from the secondary circuit is again transformed into water because of a condenser in which cold water from the sea or a river flows. This third circuit is called the cooling circuit – at the riverside, the water in this circuit can be cooled by contact with the air circulating in the air coolers (source: www.edf.fr). 5.3.2.1. Neutronics The design of a reactor has different applications: power generation in power plants, submarine propulsion or experimental projects. It includes a phase during which the mechanisms of the nuclear reaction are studied. Christophe Calvin, an expert in numerical simulation at the CEA, has participated in the development of numerical simulation codes for reactors. He explains how numerical simulation contributes to assessing their performance and safety: “The objective of neutron modeling is to develop ‘calculation schemes’ adapted to a given reactor type (pressurized water, boiling water, sodium) in order to study nominal and accidental operating conditions. The calculation scheme makes it possible to represent the key elements of the reactor: its geometry, the type of fuel used, the presence of neutronabsorbing materials. The data from the simulations allow the analysis of different reactor operating scenarios. In particular, they contribute to the demonstration of the performance required by an industrial company or a nuclear energy safety authority”. The input data of neutron computation are those of the probability of interaction of one particle with another, as a function of their respective energies. These data, derived from fundamental physics experiments, are obtained through international

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scientific collaborations. Shared by the various contributing countries, they are updated regularly according to the evolution of knowledge. Two families of methods are deployed by neutron simulations: – Probabilistic methods consist of performing the propagation calculations of reactions, describing particle-by-particle energy interactions and the formation of new nuclear species. Based on modeling without physical bias, they are very accurate, as well as very expensive in terms of computation time. These methods are generally used for research or expertise purposes and less in the context of operational monitoring. – The deterministic methods use, like probabilistic methods, a transport equation describing neutron dynamics. Each physical quantity , whose evolution in time and space is monitored, follows an equation written as: +

∙ ∇ = ( , , ),

where represents the velocity field of the particles, / and variations in time and space and ( , , ) all interactions and reactions. The simulation is based on a numerical method ensuring the calculation in time and space of the quantity . The transport equations are “linear”, a mathematical property used to decouple problems and to calculate very quickly the different steps of neutronic processes. “The simulation is then carried out in two steps. The first is a twodimensional calculation: a fine model represents a horizontal section of the reactor, representing the core and the fuel elements of which it is made (usually an assembly of rods containing the fissionable elements). The second one gives access to the different states of the core on its height, the third dimension, using the data from the previous calculations. This approach gives satisfactory results – and the calculation of the steady state of a reactor can be performed in a few minutes on a standard laptop computer!” The assembly step between 2D models (Figure 5.10) and the 3D model is one of the most crucial in industrial simulations.

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Figure 5.10. 5 Power map m of a presssurized water reactor r [CAL 11]. 1 For a colo or version of this figure, see ww ww.iste.co.uk/s /sigrist/simulattion2.zip

COMMEN NT ON FIGUR RE 5.10.– Th he figure rep presents the result r of a nneutronic calculatiion performedd on a horizoontal section of a pressurrized water reeactor. It shows thhe geometry of the core, maade up of fuell elements orgganized in cluusters and immerseed in the primaary fluid. Thee calculation shows s the calcculated powerr map: in the centeer, the nucleaar reaction iss more intensee than on thee edges and thhe power developeed is thereforee more importtant. Enginneers generallly combine several s models. 2D calculaation data are used for many othher 3D models based on sim mplified or ho omogenized traansport equatiions. “A ‘calculation scheme’ s is maade up of all th he data and toools necessaryy for o the core: itt includes thee list of situattions studied, the the simulation of calcculation codees used for 2D D and 3D mo odeling, the computer libraaries neccessary for itts execution. It is a turn nkey tool delivered to design enggineers; it is subject to audiit procedures by its users and a nuclear saafety authhorities. It is a question of limiting l its usse and guarantteeing the valiidity of the data it allows us too obtain. Reaactor calculation schemes are m tools faster, connstantly being improved: thhe aim is to refine models, make and eassier to operaate and morre versatile, combining probabilistic p deterministic appproaches”. 5.3.2.2. Thermohydrraulics Neuttron calculatioon makes it possible p to ev valuate the power p produceed in the reactor core; c this power is evacuateed into the prim mary fluid, ussually water orr sodium, which trransports it too the heat excchangers with h the secondarry circuit (Figgure 5.9). The heatt transfer is reepresented usinng thermohyd draulic modelss that take intoo account

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the circuulation of the fluid f in the reaactor and the various v heat trransfers that ttake place there. “Thhermal-hydrauulic simulatioon contributess to reactor design d and saafety studdies. It makess it possible too understand the t operation of o the reactor in a norrmal situationn, to evaluatee the consequ uences of a design d choicee, to studdy transient phases, p duringg which the power to be delivered by the reactor may varyy...”. In noormal operatioon, a reactor operates in fo orced convecttion: the circuulation of the heat transfer fluidd is ensured by b a pump, an a element exxternal to the vessel in ded speed corrresponds, for example, which thhe nuclear reaction takes place. A degrad to the suudden stop of this pump. Under these conditions, the t reactor opperates in natural convection, the t fluid flow w is established accordinng to the tem mperature conditionns and the eneergy producedd by the core. “Siimulation is used u to study degraded reg gimes and ansswer these saafety crittical questionss. How does convection c move m from the forced regim me to its natural regim me? Is it suffficient to cirrculate the prrimary fluid and evaacuate the poower produceed by the core, c as the mechanisms for reggulating and modulating m thee neutron reacttion are put inn place? Is theere a riskk of the reactoor boiling?” Therm mal-hydraulicc simulations are based on fluid dynamiics calculationns, taking into accoount thermal effects e (Figuree 5.11).

Figure 5.11. 5 Multiscalle thermo-hydrraulic calculattions of a 4th generation g rea actor core (source: calculation performed p with h the CATHARE system co ode, the Trio--MC core code and the TrioCFD D CFD code – ©CEA/Direction de l'Éne ergie Nucléairre). For a color verrsion of this fig gure, see www w.iste.co.uk/sig grist/simulation2.zip

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COMMENT ON FIGURE 5.11.– The code architecture for understanding and simulating the thermohydraulics of reactor cores has been designed to develop as generic a tool as possible. The development of the tools is the result of the collaboration of many experts: physicists, mathematicians and engineers who work together to validate development choices. They combine various approaches that make it possible to report on global fluid circulation phenomena, as well as finer flow models in the vicinity of the various components of the reactor. “Turbulent phenomena come into play in the thermohydraulics of reactors. However, the finest models, such as provided in LES simulation (representing large eddies in turbulence), are not necessary in all areas of the reactor: simulations span different approaches, which is more efficient! The challenge is then to make different flow models (1D, 2D or 3D) coexist with different turbulence models. Expertise that is collectively held by different experts...” NOTE.– Representing heat exchanges accurately. In a reactor, the heat exchanges between the core and the primary fluid guarantee its operation. They occur in the vicinity of the fuel elements and local flow conditions greatly influence them: the most homogeneous fluid flow possible is favorable to them. Mixing grids, made of metal fins, disturb the flow to obtain the desired conditions. Turbulence is developing fully and can only be accurately represented with appropriate modeling. The simulation allows us to validate a design and the complete choice of tests performed on a test device representative of the mixing zone. Representing very finely the experiment, the calculation reproduces the geometry of grids and fins and turbulent phenomena at small scales (Figure 5.12). “Such simulations require significant human and computer resources. Reaching an unprecedented level of accuracy, they require several weeks of mesh preparation time; they then mobilize nearly 10,000 cores on supercomputers for several months, and their analysis still requires several months of work on the part of experts!”

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Figure 5.12. Calculation of the LES in an reactor mixing grid (source: Christophe Calvin/Commissariat à l'Énergie Atomique). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 5.12.– The figure shows an LES calculation of fluid flow through mixture grids in a reactor core. It displays the flow rate with different colors, corresponding to fluid flows calculated at different times. It thus illustrates the fact that the flow is totally “chaotic”, both in the three dimensions of space and also in time. 5.3.3. Developing nuclear fusion Fusion is the nuclear reaction that feeds our Sun and is an almost inexhaustible source of energy. With a very low impact on the environment, its control would be a response to many of humanity’s energy needs in the 21st Century... and beyond? It occurs in plasmas, the environment in which light elements can combine and produce energy. Plasma is sometimes presented as the fourth state of matter. These environments are found, in particular, within the stars (Figure 5.13). A fusion plasma is obtained when a gas is heated to extreme temperatures in which the electrons (negatively charged) are separated from the nuclei of the atoms (positively charged). Experimental devices aim to artificially recreate conditions on Earth that are favorable to fusion reactions. In particular, magnetic confinement fusion plasma is a tenuous environment, nearly a million times less dense than the air we breathe.

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Figure 5.13. The energy of the Sun and stars comes from the fusion of hydrogen (source: www123rf.com/rustyphil)

COMMENT ON FIGURE 5.13.– What we perceive as light and heat results from fusion reactions occurring in the core of the Sun and stars. During this process, hydrogen nuclei collide and fuse to form heavier helium atoms – and considerable amounts of energy. Not widely distributed on Earth, plasma is the state under which more than 99.9% of the visible matter in the Universe occurs. There are different types of plasmas: cold (to a few hundred degrees) or very hot, dense (denser than a solid) to thin (more diluted than air). The core plasmas of magnetic confinement fusion machines are thin (about 100,000 times less dense than ambient air) and very hot (about 150 million degrees). In the core of stars such as the Sun, fusion occurs at much higher densities (about 150 times that of water) and at temperatures about 10 times lower (source: www.iter.org). The temperature is such that it partially overcomes the repulsion forces opposing different charge particles and thus allows the material to fuse. The ITER machine, for example, is one of these: its objective is to control fusion energy. Involving 35 countries (those of the European Union, the United States, India, Japan, China, Russia, South Korea and Switzerland), it is one of the most ambitious global scientific projects of our century3. It is a step between the research facilities that preceded it and the fusion power plants that will follow it. The Cadarache site in France, near the CEA center, has been hosting ITER facilities since 2006. It should host a first plasma in 2025 and carry out controlled 3 Initially acronym of International Thermonuclear Experimental Reactor, ITER nowadays refers to the Latin word for “path” – designating the way to be followed by scientists working to control nuclear fusion energy?

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fusion reactions by 2035. ITER is a “tokamak”, a Russian acronym for a magnetized toroidal chamber: the conditions conducive to fusion are obtained by magnetic confinement (Figure 5.14). In a tokamak, the particles have a helix-shaped trajectory around the magnetic field lines that wind around virtual interlocking toroidal surfaces. The temperature in the plasma core is in the order of 10–20 kilo-electron-volts (keV) – these are extremely high values, with 1 keV representing more than 10 million degrees Celsius! It falls to a few eV (1 eV corresponds to about 11,000 °C) near the walls of the tokamak. Yanick Sarazin, a physicist at the CEA’s Institute for Research on Magnetic Containment Fusion, explains one of the challenges of current fusion research: “The gigantic temperature differences between the reactor core and the walls make the plasma of the thermodynamic systems ‘out of balance’. They naturally tend to approach a situation of thermal equilibrium by dissipating the heat within them: we speak of ‘relaxation’. Turbulence in the plasma contributes significantly to these heat losses. One of the objectives of the tokamak design is to force the organization of turbulence, so that relaxation takes place slowly. It is, among other things, under these conditions that fusion performance will be economically viable”.

Figure 5.14. Obtaining a plasma in a device: example of the European JET “tokamak” before and during its operation (source: www.iter.org). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 5.14.– Three conditions must be met to achieve fusion in the laboratory: a very high temperature (to cause high-energy collisions), a high plasma particle density (to increase the probability of collisions) and a long containment time (to maintain the plasma, which tends to expand, in a defined volume). The fusion reaction can be obtained in a machine using very intense magnetic fields to confine and control the hot plasma: the giant ITER coils thus deliver fields of a few tesla, nearly a million times the Earth’s magnetic field (source: www.iter.org). Numerical simulation is the tool of choice for researchers to understand the origin of turbulence in tokamaks – and to predict and control it in order to limit heat loss. Plasma physics is fundamentally described by the equations of MagnetoHydro-Dynamics (MHD), which can be seen as the coupling between the NavierStokes (Box 2.1) and Maxwell equations (Chapter 2 of the first volume). Unfortunately, three-dimensional numerical simulations of the MHD are insufficient to describe the turbulent heat transport processes in these highly diluted and very low collision environments. The researchers then work with kinetic models based on the Boltzmann equation, already discussed in Chapter 2. The calculations focus on the evolution of the charged particle distribution function, which measures the probability of finding them in a given volume of 6-dimensional “phase space”. The phase space is made up of the three position variables and three particle velocity components – in practice, an additional assumption reduces the problem to five components of the phase space, whose evolution over time is monitored. The characteristic flow quantities (mass, amount of movement, energy, etc.) are obtained by calculating the weighted averages of the distribution function. The resolution of kinetic equations coupled with Maxwell equations is based on different methods: – Lagrangian methods consist of calculating the distribution function as a result of the dynamics of microparticles, whose interaction, described with the Newton equation, defines their trajectory. This method is well suited to parallel calculation but has its limits in the case of turbulent flows, where trajectories become chaotic and are more difficult to calculate. This can lead to a loss of information in some regions of the phase space. This results in “numerical noise”: disrupting calculations, it can nevertheless be reduced by dedicated techniques; – Eulerian methods consist of calculating the distribution function on a fixed grid of the phase space, using discretization methods as described in Chapter 1 of Volume 1. It makes it possible to comply, more accurately, with the conservation conditions but loses its effectiveness when implemented in a parallel computer.

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An intermediate method, called Arbitrary Lagrange-Euler or ALE, encountered in Chapter 2 concerning fluid-structure interactions (Box 2.2), is adapted to the resolution of MHD equations in the Boltzmann statistical formalism, by separating the resolution of flow equations, treated in an Eulerian manner at the current time step, and electromagnetic equations, treated in a Lagrangian manner at the previous time step. Virginie Grandgirard, a computer scientist at the CEA’s Institute for Research on Magnetic Containment Fusion, details the difficulties encountered in the simulations: “Even with the most efficient numerical methods, such as the ALE approach, simulations are constantly limited by computational means. GYSELA, the calculation code developed at the CEA to simulate turbulence in tokamaks, uses the largest French and European computers: a complete simulation of the physical phenomena we want to study requires nearly a week of calculation on 16,000 to 32,000 processors!”

Figure 5.15. Simulation of turbulence developing in a tokamak. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 5.15.– The simulation represents an instant map of the turbulent structures calculated in a tokamak plasma, visualizing the electrical potential. Carried out with the GYSELA code, developed at the CEA center in Cadarache, France, the simulation makes it possible to visualize how the eddies stretch along the magnetic field lines [GRA 16]. It helps researchers understand the dynamics of turbulence in tokamak plasma and how it influences heat transfer (source: Yanick Sarazin and Virginie Grandgirard, Office of the Commissioner for Atomic Energy and Alternative Energies).

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HPC calculation (Chpater ( 3 off the first vollume) is thereefore a cruciaal tool to r inn their understtanding of fussion physics. In I order to remove the support researchers technical obstacles poosed by the control c of tom morrow’s nuclear energy, iit will be necessarry to change the scale in the power off the computeers. The quesst for the Exascalee has only jusst begun, and because of itss strategic natture for fusionn control, the GYS SELA code iss one of the tools used by y the Europeaan EoCoE-II project – which aims a to suppoort the portinng of the calcculation codees used by thhe energy communnities to the exxa-flop ECU class. c The adap ptation of a caalculation codde to such computeers requires the collaborration of ex xperts from different disciplines: theoreticcal and applied physicistss, computer scientists, s sim mulation expeerts, code developeers and users. The energy of o the 21st Cen ntury will alsoo depend on tthe fusion of multipple scientific skills! s 5.4. New w energies Driveen by an awaareness of ecoological issuees, the search for alternativve energy sources – wind, waves, sun, heat frrom the sea, laand or waste – as opposed tto carbon and urannium continues to grow (Figgure 5.16).

Fig gure 5.16. Glo obal investmen nt in renewablle energy (sou urce: Our Worlld in Data/h https://ourworld dindata.org/renewables). Fo or a color verssion of this figu ure, see www.iste.co o.uk/sigrist/sim mulation2.zip

COMMEN NT ON FIGUR RE 5.16.– In 2004, globall investments in renewablle energy amounteed to $47 billiion, reaching $286 billion by 2015, an increase that could be seen in all a regions of the t world, albbeit at differen nt levels. The largest l increaase was in

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China: from $3 billion in 2004 to $103 billion in 2015, investment in China increased more than 30-fold – compared to the global average of 7 billion. China is nowadays the most significant investor in renewable energy, with its financial capacity representing that of the United States, Europe and India combined. 5.4.1. Hydroelectricity In the Chinese city of Fengjie, on the Yangtze River, a man and a woman meet in search of their past. A past that the city will engulf, once submerged by the gigantic Three Gorges Dam. With his film Still Life, Chinese filmmaker Ja ZhangKé tells a nostalgic story, whilst questioning the meaning of the long march of Chinese economic development [ZHA 07]. It is set against the backdrop of the construction of one of the largest civil engineering structures of our century (Figure 5.17). Located in the mountainous region of Haut-Yangzi, the 2,335-m-long and 185-m-high Trois-Gorges dam came into service in 2009, after more than 15 years of construction. Its electricity production covers less than 5% of China’s energy needs, the world’s largest hydropower producer ahead of Canada, Brazil, the United States and Norway – countries crossed by many large rivers and streams and thus benefiting from an abundant resource.

(a) Overview

(b) View of the tank Figure 5.17. The Three Gorges Dam (source: www123rf.com)

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COMMENT ON FIGURE 5.17.– A hydroelectric power plant consists of a water intake or reservoir, as well as a generating facility. Over the distance between the dam and the power plant, water passes through a canal between the intake and return points, a gallery or penstock. The greater the difference in height, the greater the water pressure in the plant and the greater the power produced. The amount of energy is proportional to the amount of turbinated water and the height of fall. The Three Gorges Dam reservoir stores nearly 40 billion m3 of water, the equivalent of 10 million Olympic swimming pools, and covers more than 1,000 km2, the equivalent of 100,000 football fields. The waterfall height, about 90 m, represents a discharge capacity of more than 100,000 m3/s. The capacity recovered by the 30 turbines of the Three Gorges Dam amounts to 22,500 MW, seven times the capacity of the Rhône hydroelectric power stations (in France), estimated at 2,950 MW. The energy transported by the flow is recovered by means of turbines (Figure 5.18), a device invented at the dawn of the 20th Century by French engineers Claude Burdin (1788–1873) and Benoît Fourneyron (1802–1867). Exploiting their patent and improving their invention, the French engineer Aristide Bergès (1833–1904) created, in 1882, one of the first electricity production plants on the Isère River in France.

Figure 5.18. Francis turbine (1956), at the leading edges of cavitation-eroded blades (source: www. commons.wikimedia.org)

Since their first use, turbines have been constantly adapted to the applications for which they are intended by engineers. The current machines are designed to meet the challenges of renewable energy. Guillaume Balarac, a researcher in fluid mechanics and their applications to hydraulics, explains:

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“The energy produced by exploiting certain renewable resources is intermittent and hydropower is increasingly required to be able to absorb the fluctuations in solar and wind power production. As a result, hydroelectric turbines are operating at new speeds far from their nominal design points. Marked, for example, by large fluctuations in hydraulic loads or low loads, flows in these regimes are often very unstable and characterized by complex physical phenomena, such as turbulence or cavitation”. Cavitation develops when the pressure drops below the threshold where the gases dissolved in the fluid remain compressed. As when opening a bottle of champagne, bubbles are formed that affect the flow characteristics and efficiency of the turbine. Very unstable, these bubbles can also implode by releasing a significant amount of energy into the liquid. The shockwave resulting from the implosion then becomes sufficient to damage solid surfaces. As a result, cavitation erosion (Figure 5.18) is a major concern for turbine or propeller designers, significantly reducing their service life. “Numerical simulation allows us to understand the new operating modes of turbines and helps to broaden their operational ranges. The appearance of eddies, or cavitation, clearly modifying the efficiency of the turbines, the models aim to accurately represent the physics of flows, and in particular, turbulence. Statistical methods, deployed in the average modeling of Navier-Stokes equations (RANS), have their limitations here. The calculations are based on large-eddy models (LES), which are much more representative of turbulent dynamics and the pressure fluctuations they generate”. With large-scale simulations, researchers and engineers are better able to predict flow trends. By more precisely analyzing the causes of yield loss with the calculation, they can also propose new concepts or optimize existing shapes [GUI 16, WIL 16]. Calculations require fine mesh sizes to be able to capture physical phenomena on a small scale (Figure 5.19) and restitution times increase proportionally. LES models produce a large amount of data, in particular the velocity and pressure at each point and at each time step of the calculation. This information is then used to analyze the flow, using statistical quantities (average velocity and pressure, and the spatial and temporal fluctuations of these fields, turbulence energy, etc.), close to those that an experiment would provide. These are obtained at the cost of long calculations, sometimes lasting a few months! The complete simulation of a turbine using LES models is still not possible, so calculations focus on the machine

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body. Inn order to accoount for the fllow conditions at the turbinne inlet, they aare based on experrimental data, or calculatedd using less ex xpensive methhods, such as in RANS method.

(a) 4 millio on cells

(a) 80 million m cells

Figure e 5.19. Mesh size s used for LES L simulation n of a turbine body b [DOU 18 8]. For a color version of this figure, see www.iste..co.uk/sigrist/ssimulation2.zip p

COMMEN NT ON FIGUR RE 5.19.– The e figure show ws the mesh used u to simuulate flow around a turbine bladde with LES modeling. m Thee first calculattion, performeed on a 4 million cell mesh, has h a low sppatial resoluttion and doees not capturre vortex formatioon in the vicinnity of the blaade. Based on a mesh sizee of nearly 880 million cells, the second onee has sufficieent resolution n to finely siimulate the fl flow. LES v expensivee in terms off modeling, caalculation andd analysis calculatiions remain very time. Foor industrial applications, they are ofteen used in coonjunction wiith RANS models. Taking advanntage of nearr-wall RANS models m and LES L models inn regions further away a from theem, DES (Detaached Eddy Siimulation) meethods make itt possible, for exam mple, to accurately represeent flows in the presence of obstacles, at more accessibble calculationn times than LE ES models can n offer [CAR 03]. Whille these LES calculations are not yet in ndustrially appplicable, theyy provide valuablee guidance to turbine t designners: “W With LES models, m for exxample, we haave identifiedd areas of higgh ennergy dissipaation due to innstabilities in n observed floows for verticcal axxis turbines. In I an attempt to reduce thee formation off these turbinees, w have prooposed a neew design for we f these turrbines througgh siimulation...”

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5.4.2. Wind energy Recovering the energy contained in the wind is the challenge that engineers are also trying to meet: offshore wind energy, for example, is developing in various regions of the world and various projects are being developed. The preferred locations for installing farms are those with good wind conditions (Figure 5.20).

Figure 5.20. Offshore wind turbine fields (source: www123rf.com/Wang Song)

COMMENT ON FIGURE 5.20.– A wind turbine is a turbine set in motion by the forces exerted by a flow on its blades. The shape of these is designed to separate the air flow and accelerate it differently depending on the face of the blade profile: the more strongly accelerated flow exerts a lower pressure on the profile than the less accelerated flow. This pressure difference generates a driving force on the blades and sets them in motion. The mechanical energy due to their rotation is then converted into energy made available on an electrical grid. The power theoretically recoverable by a wind turbine depends on air density, blade size and flow velocity. For a horizontal axis wind turbine, the theoretically recoverable power is proportional to the square of the diameter of the turbine and the cube of the wind speed. The largest onshore wind turbines, whose diameter is generally between 130 and 140 m maximum, develop powers in the range of 2–4 MW; offshore wind turbines, with a larger diameter (typically between 160 and 180 m), deliver a nominal power in the range of 6–8 MW depending on wind conditions. Horizontal axis wind turbines are nowadays much more widespread than vertical axis wind turbines. The latter are a potentially preferable solution to the former in two niche sectors: – urban environments, because they behave better in changing and turbulent wind conditions;

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– the marine environment, as they can have interesting characteristics for floating wind turbines. In a vertical axis wind turbine, the electricity generator can be placed close to the water level, which facilitates maintenance operations, and the center of gravity is lower, which improves the stability of the floating structure. Vertical axis wind turbines operate at generally reduced rotational speeds, which can lead to “dynamic stall” under certain conditions. Similar to a loss of lift for an aircraft wing, it involves more complex, highly unsteady and intrinsically dynamic physical phenomena for this type of wind turbine: in particular, a release of eddies interacting with the blades is observed. These phenomena result in a significant decrease in the wind turbine’s efficiency. Numerical simulation provides a detailed understanding of the nature of air flows, and helps to anticipate the risks of boundary layer detachment in low velocity flow regimes. Laurent Beaudet, a young researcher and author of a PhD thesis on the simulation of the operation of a wind turbine [BEA 14], explains: “My work has helped to improve numerical models for predicting detachment for a vertical axis wind turbine. I have developed a calculation model based on the so-called ‘vortex method’. This allows any type of simulation of load-bearing surfaces, such as helicopter blades, wind turbines, etc., to be carried out and to represent these surfaces and the vortex structures developing in their wake. Potentially applicable to various wind turbine concepts, it is a particularly interesting alternative to 'traditional' CFD calculation methods, such as deployed in RANS or LES simulations, in terms of calculation costs in particular”. This method is becoming increasingly important in the wind energy sector, with different types of applications for which it is effective: “In order to support the development of increasingly large and flexible offshore wind turbines, it is necessary to couple an advanced aerodynamic calculation module with a structural dynamics solver and a controller. The analyses of wind turbine load cases, necessary for their certification, are based on such ‘multi-physical’ models. For these simulations, representing both the flow, motion and deformation of the blades, and the actuators/motors of the wind turbine, optimizing the calculation times is crucial and the vortex method meets this need”.

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Figure 5.21 1. Flow calcula ation around a vertical axis wind turbine (source: In nstitut P'/ httpss://www.pprim me.fr/). For a co olor version of this figure, see ww ww.iste.co.uk/s /sigrist/simulattion2.zip

COMMEN NT ON FIGURE E 5.21.– The figure f illustrates the simulaation of a verrtical axis wind turrbine (the “N Nov'éolienne”,, developed by b Noveol), using a vortexx method, implemeented in the GENUVP G calcuulation code (GENeral Unnsteady Vortexx Particle code). This T tool, oriiginally develloped by the National Teechnical Univversity of Athens (NTUA), alllows aerodyynamic simu ulations for a wide vaariety of configurrations and appplications. Thhe models useed for this typee of calculatioon have a wide scoope and are off interest to many m applicatiions. It shouldd be noted thaat vertical axis wind turbines havve not yet reaached sufficien nt maturity annd reliability tto be able m – in paarticular theirr service life remains very ry limited to be deeployed en masse because they are subjeect to high fattigue stresses. A caapricious resouurce, wind exxhibits great variations v in speed, s time annd space. This dispparity conditioons the investtments requireed for farm prrojects, both aat sea and on land, or the installaation of wind turbines in urb rban areas. The power delivvered by a g for winnd speeds betw ween 3 and 10 1 m/s, and reeaches an wind turrbine varies greatly almost constant c valuee above 10 m/s. m In this interval, the slightest s flucttuation in speed caan result in siggnificant yieldd losses and the task of winnd project enggineers is to find the t siting areaas where windd speed is thee highest and turbulence thhe lowest. Stéphanee Sanquer, Deeputy General Manager of Meteodyn, M expplains: “S Site data is esssential in the design of a wind w power prroject. They aare usually obtaineed by dedicateed devices, su uch as a measuuring mast. Thhe v expensivee, it is generallly opperation of suuch instrumenttation being very im mpossible to base a site analysis a on th his method alone. Numericcal

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simulation makes it possible to complete in-situ measurements. To this end, we have developed an ‘expert tool’, dedicated to wind simulations on complex terrain (mountainous, forest, urban areas, etc.). Calculations allow a relationship to be established between the data from on-site measurements at a given point and any other point on the site. Based on information on the measurement point, wind statistics in ‘average meteorological’ conditions, or more exceptional conditions (such as storms), the simulation reconstructs the corresponding mapping over the entire fleet”.

Figure 5.22. Wind measurement mast on a wind site (source: Le Télégramme/https://www.letelegramme.fr)

Proposing a global approach to the wind power project [CHA 06, DEE 04, LI 15], the calculation methodology is based on: – an implementation database. This describes in particular the land cover, i.e. the roughness and characteristics of the terrain, which have a major influence on local wind conditions; – a solver for flow equations (stationary Navier–Stokes model). The latter report on turbulence and thermal effects using models specific to atmospheric physics.

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Based onn the finite voolume methodd, the solver uses u efficientt numerical m methods: a calculatiion for a givenn wind directiion requires a few hours onn “standard” computer resourcees. A compleete wind mappping, explorring differentt cases of innterest to engineerrs, is thus obttained in a callculation timee compatible with w the scheedule of a project; – a module m for annalyzing the calculation c results. It is caarried out according to specific criteria, usefuul to engineerrs and adapteed to wind ennergy projects (such as v of windd speeds, energy productioon over a giveen period average or extreme values g areas of the site). and on given

(a) Numerical N calcculation mode el

(b b) Projection of o results on ssite

Figure 5.23. 5 Evaluatio on of a site’s wind w resource (source: calculation carried d out with the Mete eoDyn/WT6 so oftware by the e company Me eteoDyn/www..meteodyn.com m). For a color version of this figure, see www.iste..co.uk/sigrist/ssimulation2.zip p

The calculations c p provide additioonal expertise to the measurrements and ccontribute to a bettter estimationn of the perfoormance of th he future insttallation. Ensuuring the production of a wind farm f is a cruccial element an nd simulation has become oone of the ments in the developmeent of a wind energy investment i plan. The key elem developm ment of windd turbine farm ms poses maany technical challenges, including understaanding the inteeraction between a wind tu urbine’s wakee and its neighhbors and the yieldd losses it causes. In ordder to study such phenom mena, researcchers and engineerrs implementt complex flow simulaations, using dedicated methods, hybridizing mean turrbulence moddels (RANS) or large-scaale turbulencee models (LES). The uses u of numerrical simulatioon in the field d of energy, off which we haave given some examples in thiss chapter, covver a large num mber of appliccations and prroblems – they extend in particuular to buildinngs, with thee aim of savinng resources, reducing ht (Figure 5.244). energy loosses or evaluuating the effeects of sunligh

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Figure 5.24. Evaluation of the effects of sunlight on an urban area using dynamic thermal simulations (source: www.inex.fr). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 5.24.– The “dynamic thermal simulation” of a building is the study of the thermal behavior of a building over a defined period (from a few days to 1 year) with an hourly, or lower, time step. The modeling aims to account for all parameters affecting the heat balance, such as internal and external heat inputs, building thermal inertia, heat transfer through walls, etc. Models describing thermal phenomena require knowledge of geometric data (such as wall thickness, shape of thermal screens, etc.) and material characteristics (such as coefficients describing their ability to store or propagate heat). Dynamic thermal simulation makes it possible to estimate the thermal requirements of buildings in operation, taking into account, for example, the various thermal inputs and the behavior of the occupants and the local climate. Among the external thermal inputs, sunlight receives particular attention from architects, design offices, etc. The simulation can then be used to design buildings according to different criteria (minimize or maximize solar gains or seek optimal protection) and supports their energy optimization. As emphasized in Chapter 3 of Volume 1, numerical simulation is somehow an energy-consuming technique. However, examples given in this chapter also suggest that it has gradually become a major asset to tackle challenges in all energy sectors. It opens now to new application areas, such as biomechanics.

6 The Human Body

Jean-Baptiste Poquelin – or Molière as he is more widely known as – (1622– 1673), is one of the most famous French playwrights in the world. Performing the main role in most of his plays, he explored all the resources of comedy theater. Suffering from a lung disease, he died from a stroke he had on stage, while performing his last play, Le Malade Imaginaire [MOL 73]. Molière was wary of doctors at the time: the remedies they proposed had as much chance of curing a patient as they did of speeding up his death. The figure of the aging practitioner imbued with outdated knowledge appears in several pieces. Thus the character of Diafoirus, administering care to Argan, a hypochondriac, who, for his part, dreams of becoming a doctor. The final painting of the play features him as he takes the exam opening the doors of the profession. To university teachers who ask him about cures for all kinds of diseases, his answer is invariably: enema, bleeding and purging. What if the disease persists? The same cure! These answers earned him the ovations of the jury, a choir enthusiastic to welcome a new member worthy of practicing the respectable profession. To reinforce the solemnity of the examination, and to insist with humor and irony on the ridicule of the characters, Molière wrote in Latin: “SECONDUS DOCTOR – Quæ sunt remedia quæ in maladia ditte hydropisia convenit facere? BACHELIERUS – Clysterium donare postea seignare ensuitta purgare. TERTIUS DOCTOR – Quæ remedia eticis, pulmonicis, atque asmaticis trovas à propos facere. BACHELIERUS – Clysterium donare postea seignare ensuitta purgare. QUARTUS DOCTOR – Et pena de respirare: Veillas mihi dire, Docte Bacheliere, Quid illi facere? BACHELIERUS – Clysterium donare postea seignare ensuitta purgare. QUINTUS DOCTOR – Si maladia opiniatria non vult se garire quid illi facere?

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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BACHELIERUS – Clysterium donare postea seignare ensuitta purgare, reseignare, repurgare, et rechilitterisare. CHORUS – Bene, bene, bene, bene respondere: dignus, dignus est entrare in nostro docto corpore!” [MOL 73]1. 6.1. A digital medicine The medicine that Molière mocks is not that of the 21st Century: like many other sciences, it has broken with Diafoirus through innovative approaches. It evolves in relation to other areas of research and knowledge, and benefits from the contributions of new techniques. Applied mathematics and digital mathematics extend the knowledge accumulated by physicians over a long period of time (Figure 6.1). They are an integral part of the techniques used for health research, which is at the interface between medicine, physiology, biomechanics, physics, biology and imaging. As explained by Anne-Virginie Salsac, researcher at the CNRS*: “Three main methods now make it possible to increase the understanding of living organisms: ‘in vitro’ experiments (on experimental devices representative of living organisms), ‘in vivo’ tests on animal models (mice, pigs, sheep, etc.) or human models (clinical tests, etc.), and ‘in silico’ modeling. The latter have two main objectives: the first is to contribute to the understanding of the mechanical behavior of the human body under physiological and pathological conditions to help explain degenerative processes, diagnosis and planning of medical procedures; the second is to allow the development of medical devices (prostheses, catheters, heart valves, etc.).”

1 This may be naively translated in the following terms: SECOND PHYSICIAN – What are the appropriate remedies for this disease called dropsy (water retention)? CANDIDATE – Perform an enema, then a bleed and a purge. THIRD PHYSICIAN – What remedies do you think are appropriate for asthma and pneumonia? CANDIDATE – Perform an enema, then a bleed and a purge. FOURTH PHYSICIAN – And for respiratory failure, would you tell me, aspiring doctor, what you would recommend? CANDIDATE – Perform an enema, then a bleed and a purge. FIFTH PHYSICIAN – And if the disease persists, if the patient does not heal, what should be done? CANDIDATE – Perform an enema, then a bleed and a purge; again a bleed and a purge... . CHORUS – Good, good, good! He is worthy to join our learned corporation!

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Figure 6.1. Excerpt from Jean-Baptiste Sénac’s book, Traité de la structure du cœur, de son action et de ses maladies, Éditions Méquinon, Paris, 1783 (source: www.biusante.parisdescartes.fr)

In vivo experiments have been part of biomedical research since its earliest origins: in ancient times, the first Greek scientists interested in medicine, such as Aristotle (384–322 BC) and Erasistratus (304–258 BC), learned through experiments on live animals. Ethical debates on animal testing have been ongoing since the 17th Century. Nowadays, the sacrifice of animals, made necessary for certain research tests, is the subject of strong criticism from groups of citizens involved in animal protection and the defense of their rights. Various countries, including France, are legislating to regulate practices and, if they cannot yet do without them completely, to ensure animal welfare [HAJ 11]. Numerical simulation helps to integrate these ethical concerns into scientific research, as Jean-Frédéric Gerbeau, a researcher at INRIA*, explains: “Digital simulation makes it possible to prepare in vivo test campaigns and significantly reduce the use of experiments on living organisms. It also offers researchers the possibility of developing alternative models to living organisms, by validating ‘in vitro’ devices or by carrying out ‘in silico’ experiments.” Let us also note that in vivo tests include experiments to which human beings consent. The development of cardiac prostheses and their approval by health

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authorities requires the demonstration of their safety and robustness, established in particular by implantations on voluntary patients [COU 18, EDW 18]. The difficulties in modeling the human body are as follows: – the mechanical behavior of human tissues and organs is heterogeneous and anisotropic – and, in most cases, it is necessary to use “complex” behavior laws (blood behaves like a non-Newtonian fluid, liver deformations are described by a viscoelastic model, for example); – the geometry of the human body varies greatly from one patient to another and is not standardized: it is necessary to develop algorithms capable of quickly producing models adapted to each patient by identifying the different anatomical parts (skin surface, bone, fat, muscles, etc.) on medical imaging data; – the boundary conditions to be applied to a biomechanical model (efforts on a tissue, muscle or tendon; pressure or velocity of air, blood, etc.) are not easily accessible to modelers. They also have a great influence on the calculation result and one of the major challenges of the models is to represent as realistically as possible different biophysical phenomena at the limits of the models; – the reference configuration of the human body is not easily characterized. Operating at slightly higher pressure than its environment, it is in a naturally deformed configuration. The shape of the blood vessels “at rest”, in the absence of a stress field, is not known and a return to a neutral configuration is not easily achieved. In the biomechanical field, simulation is still a research and development tool, summarizes Anne–Virginie Salsac: “With the tools currently available, researchers are calculating realistic biomechanical quantities, but we are only at the beginning of their use in hospitals. Generalizing its use requires rapid modeling and execution, and it is a matter for researchers to develop efficient and robust computational codes, a task that nowadays occupies researchers in numerical biomechanics.” In addition, a legal dimension arises: in order to generalize the use of simulation tools in the biomedical field, it is necessary to demonstrate their robustness, the way in which calculation codes are qualified in industry, and to develop current regulations – a task that has yet to be undertaken. However, biomechanical modeling has been undergoing continuous development in recent years and the future of numerical simulation is in the life sciences, according to Édouard Lété, expert in

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digital simulation at Dassault Systems and operational director of Digital Orthopaedics: “The new ‘frontier’ of numerical simulation is that of life sciences! It combines many of the latest innovations in scientific computing, such as the modeling of ‘non-linear’, ‘multi-physical’ or ‘multi-scale’ phenomena. Many mathematical models developed in fundamental sciences, such as soil or fluid mechanics, make it possible to accurately represent certain situations encountered in the human body.” The challenge of simulations is to develop digital models of organs – such as heart (Figure 6.2), liver, brain or joints – accompanying the practice of surgeons, for example by correlating a symptom with a treatment or by simulating an operation.

(a) "The Living Heart Project" develops the digital simulation of a heart [BAI 14] (source: Dassault Systèmes)

(b) Heart model obtained by 3D printing (source: www.shutterstock.com)

Figure 6.2. “In silico” model and new generation “in vitro” model. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 6.2.– Numerical simulation makes it possible to calculate realistic physical and physiological quantities for the organs studied and thus contributes to representing the functioning of some of them. “About 15 digital core model projects are underway in the world,” explains Édouard Lété. “The Living Heart Project”, initiated by the French company Dassault Systèmes, is one of them. The model is based on the electromechanical behavior of the organ, allowing

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for simulations that reproduce the natural beating of the heart. The simulation also permits virtual experiments to be carried out, for example, to develop models of synthetic organs. The latter are potentially useful in the preparation of the surgical procedure or the production of prostheses. The choice of materials and manufacturing processes is based on the analysis of medical data and a calculation that can provide the mechanical characteristics representing human tissues. “These techniques, which practitioners discover at scientific conferences, may help to renew their practices for the benefit of their patients. However, they are still at a research stage today,” explains Pierre-Vladimir Ennezay, a cardiologist specializing in vascular diseases. NOTE. – Healing humans in the digital age. In 2001, the French surgeon Jacques Marescaux achieved a first in the history of surgery. A patient, hospitalized at the University Hospital of Strasbourg, underwent a gallbladder removal, while the surgeon was in New York, more than 7,000 km away. Combining high-speed telecommunications and advanced robotics, the operation was called “Lindbergh”, in homage to aviation pioneer Charles Lindbergh (Chapter 2). The use of robots in surgery dates back to the mid1990s, when the first in vivo operation using a prototype was performed in the United States. Many robots were then developed in hospital research centers in the United States, the United Kingdom and Germany to enrich the range of operations. The best known of today’s robotic systems is undoubtedly daVinciTM, developed and marketed by the American firm Intuitive Surgery. Its use was approved by the American Administration in the early 2000s for cardiothoracic surgery, urology and gynecology [PAL 09]. Since then, the surgeon’s profession has been constantly evolving, driven by advances in robotics. Jean-Marc Baste, a thoracic and vascular surgery practitioner at Rouen University Hospital, is a case in point: “Robotics first appeared in surgery about 10 years ago. When it is practiced, it makes it possible to carry out ‘minimally invasive’ interventions, targeted on the region to be operated on. Safer but more effective than open surgery, it improves the results of delicate and complex operations, simplifies care and limits possible post-operative complications. It offers the patient the prospect of a better quality of life after an intervention.” Surgical procedures, including those performed with “minimally invasive” techniques, are prepared using digital data: in the operating room, the surgeon has

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all thee informationn in the patiient’s file on n a touch sccreen – for example, visualizations of thee area to be operated on (Fig gure 6.3).

Figu ure 6.3. The area a to be ope erated on, in th his case a tum mor, is identifie ed on a patien nt’s digital me edical imaging file (source: Jean-Marc J Basste, Rouen Un niversity Hospita al). For a colorr version of thiis figure, see www.iste.co.uk w k/sigrist/simula ation2.zip

The suurgeon operatting with a roobot visualizees the interveention area inn 3D and controlls the instrum ments with the same dexteriity as in an oppen surgical pprocedure (Figuree 6.4).

Figurre 6.4. Assisted robotic surg gery (source: Jean-Marc J Basste, CHU de R Rouen)

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A second surgeon assists him in the operation – and can take over in the event of a (very unlikely) failure of the robot. The practice requires very good coordination of medical teams (surgeons, anesthetists and nurses) and the practitioners who develop it attach as much importance to the technical and human skills of their teams. Tomorrow, the system will be able to integrate communication functionalities: the surgeon will be able to connect with other experts around the world, who will be able to follow an operation and discuss the best option to be taken during a difficult operation. More than a hundred robots are installed in the operating rooms of French hospitals. Even if this technique does not currently constitute the majority of the interventions performed on a daily basis, France is one of the European countries most equipped with robots. “The system of care organization in France has contributed to the development of this technique. This takes time and the current material investments are substantial: a robot costs nearly one million euros and an operation assisted by a robot takes as long as three conventional operations. Despite its current limitations, the practice is being refined, particularly with the involvement of young surgeons who are being trained in its practice.” Expected to become a standard in the coming decades, the innovative tools that assist a doctor do not make us forget that, when it comes to repairing the living, nothing can replace today’s human experience, whether or not assisted by modeling. 6.2. Medical data Since medical data are one of the key elements in the construction of a digital model, let us start by briefly discussing some methods for obtaining them on the living world. 6.2.1. Medical imaging Medical imaging has made tremendous progress in recent decades and is helping to change the practice of many medical specialists. Several techniques provide access to increasingly accurate data on patients’ health status or on the functioning of organs that are still largely unknown, such as the brain. Ultrasound, based on the analysis of ultrasound propagation in human tissues, is used urgently by a cardiologist, for example for cardiac output, valve filling rate, etc. The examination provides rapid diagnostic data (Figure 6.5).

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Figure 6.5. Cardiac ultrasound (source: www.shutterstock.com)

Magnetic resonance imaging (MRI) uses the magnetic properties of matter: – Anatomical MRI allows us to observe the resonance of hydrogen nuclei, which are present in abundance in water and fats in biological tissues, under the effect of an intense magnetic field. With MRI, it is possible to visualize the structure of an organ: this method can be used to diagnose cancerous tumors or to locate certain malformations (for example, in the brain, those that cause epilepsy). It makes it possible to construct an image of the chemical composition of the biological tissues explored (Figure 6.6), and thus of their nature and distribution in a living organ.

Figure 6.6. Cardiac MRI (source: www.123.rf.com/Weerapong Tanawong-udom)

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It requires more substantial resources and offers potentially more accurate information than ultrasound, such as analysis of the dimensions of the heart (overall volume, valve size, position of arteries, etc.) or tissues (to identify those that would be poorly perfused, for example). Non-invasive and painless, MRI also makes it possible to accurately describe the movement of the heart, such as torsion or contraction, and to deduce certain mechanical properties of this muscle. – Diffusion MRI is a powerful tool for measuring the movements of water molecules at the microscopic level. It is used, for example, to establish the fine architecture of neural tissue in the brain and to determine its variations at scales below the millimeter (Figure 6.7). Jean-François Mangin, a researcher at the “Neuropsin” brain study center and an expert in this technique, explains about diffusion MRI: “This imaging technique works like a real probe to understand the anatomical structures of the brain and other organs at microscopic scales. Decoding the images that cause the molecular agitation signals of water in living tissues remains a difficult task. For example, numerical simulation can help experts develop data processing algorithms: by varying different parameters in tissue modeling, we understand their influence on the signal to be analyzed.”

Figure 6.7. Identification of the main fiber bundles of the brain based on diffusion MRI (source: Jean-François Mangin, Vincent El Kouby, Muriel Perrin, Yann Cointepas, Cyrille Poupon/Commissariat à l’Énergie Atomique, NeuroSpin center). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 6.7.– Diffusion magnetic resonance imaging is used to map the brain’s “information highways”. These are the large bundles of fibers that allow neurons from different brain regions to communicate. The Neurospin center was created in France by the CEA more than 10 years ago to support the development of certain life sciences, including neurosciences. The latter are undergoing a significant evolution in their practices, due to the development of digital techniques. “This evolution is similar to that experienced by physics with the emergence of means such as particle accelerators,” explains Jean-François Mangin. “With the development of magnets capable of generating intense magnetic fields, it becomes possible to significantly improve the resolution of images from diffusion MRI and to ‘zoom into the brain’ at unprecedented scales. More than a century ago, the first studies on the brain made it possible to understand, by means of dissections, how connections between brain zones are organized. Diffusion MRI allows smaller scale mapping of connections, providing a detailed understanding of how different brain regions communicate with each other. Brain imaging also helps to change research in psychiatry. While brain structure varies from one individual to another, the analysis of imaging data does identify characteristics that are not found in the brains of some individuals, such as those who have experienced atypical neurobiological development. With diffusion MRI, for example, a first map of brain connections ‘at short distance’ was established, and the researchers found that in Asperger’s autistic people, these connections were poorly developed. Beyond the genetic factors influencing the expression of a pathology, imaging offers the possibility of understanding the origin of certain neurological diseases by means of their signature in the brain structure. A first step before being able to heal them.” The development of these imaging tools requires the collaboration of different experts: physicists, computer scientists and researchers in numerical techniques thus contribute equally with clinicians and physicians to the development of brain sciences. – The electroencephalogram (EEG) gives access to the electrical signature of the brain and the contribution of neural areas involved in a movement or perception for example. This signature is obtained by placing electrodes on the surface of the skull (Figure 6.8). – Magnetoencephalography (MEG) makes it possible to monitor the activity of groups of neurons with a very low temporal resolution, in the millisecond range – allowing complex mechanisms to be studied with great precision. This involves measuring variations in magnetic field intensity resulting from brain activity. MEG requires significant resources, currently reserved for research or medical expertise centers (Figure 6.9).

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Figure 6.8. Electrodes placed on a skull to perform an EEG (source: www.123rf.com/Dmitriy Shironosov)

(a) A seated volunteer

(b) Exercise that stimulates brain activity

Figure 6.9. Implementation of the MEG at the CEA NeuroSpin Centre (source: © P. Stroppa/CEA)

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COMMENT ON FIGURE 6.9.− No less than 300 sensors, with the sensitivity of femtotesla (10−15 tesla), continuously record the magnetic fields emitted by the currents circulating in the brain. Thus, brain activity is detected in space (on a square millimeter scale) and time (at the duration of a millisecond) to access the dynamics of the brain’s information processing. In its NeuroSpin center, CEA is also developing a new generation of MEGs based on new magnetic sensors, providing access to even finer spatial and temporal resolutions. These measurement and visualization techniques allow us to collect useful data in order to understand the complexity of the brain, linking it to the way we react or behave in given situations. They also provide an understanding of how certain areas can be damaged or how they synchronize – and what the consequences are for brain function. They can help to understand and prevent certain brain diseases or help a surgeon prepare for surgery. Visualizations of brain activity remain largely intended for study purposes: “brain imaging [...] leads to a map of the brain: it tells us ‘where it happens’ in the brain – but does not really explain to us ‘what is happening’ and ‘why’” [WAA 17]. 6.2.2. Genetic information Inspired by a novel of anticipation from British writter Aldous Huxley (1894– 1963), the film Gattaca imagines a society based on DNA testing. Orchestrated by the powerful Gattaca Aerospace Corporation, it maintains a genetic segregation of individuals [NIC 97]. In the perfect world of Gattaca, choosing a partner, accessing a profession and a social status are based on purely rational criteria. Vincent (Ethan Hawke), who is inferior due to an imperfect genetic heritage, dreams of being part of space missions open to humans with exceptional physical and intellectual qualities. He misleads the controls put in place by eugenics institution with the help of Jerome (Jude Law), who possesses all the required genetic qualities – Jerome was literally designed for this purpose.... Resigned to a wheelchair following an accident, Jerome is nevertheless unable to express them. He gives some of his genetic traces (blood, urine, bits of skin, etc.) as a contribution to Vincent’s plans – who, in turn, gives him a reason to live. First of all, fraud goes unnoticed. Unpredictability and suspicions make it apparent, jeopardizing Vincent’s project. Fortunately, for him, a final human decision is the flaw in a system where technology aims to leave nothing to chance. The conclusion of this filmed fiction allows one of its protagonists to realize his dream – and the spectator to keep hope, taking with him many questions about a possible and desirable future. Genetic engineering tools are nowadays a reality, being developed in many laboratories: the CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is one of them. It allows the DNA of plants and animals to be

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modified with great precision and can theoretically be used to prevent certain genetic diseases of the embryo [REG 15]. In 2018, research in China suggested that this tool has become operational for manipulating human DNA: have the first children with a tailor-made genetic heritage that is resistant to the AIDS virus already been born? The announcement of the work of Chinese researcher He Jiankui provides an answer and raises questions about the future of humanity [REG 18]. The DNA molecule encodes genetic information on a four-letter alphabet, those of the nucleotide bases that constitute it: A (adenine), T (thymine), C (cytosine) and G (guanine). It was discovered in the cells of living beings at the end of the 19th Century by the Swiss biologist Friedrich Miescher (1844–1895) and for a long time remained an enigma [DAH 08]. In 1953, British biologist Francis Crick (1916– 2004) and American geneticist James Watson showed that the DNA had a double helix structure [JAC 87]. Within the double helix, the DNA bases are organized in pairs, A with T and C with G. The DNA structure was visualized by Crick and Watson using an X-ray diffraction technique developed by English physicists Maurice Wilkins (1916–2004) and Rosalind Franklin (1920–1958). This discovery earned the three men the Nobel Prize in Medicine in 1962 – Franklin’s contribution had been forgotten at the time and it was only recently highlighted [LAW 18]. These DNA characteristics help understand how genetic information is copied and transmitted. Partly responsible for who we are as living people, it can also help predict what we will become in this regard – in particular the probability of developing a disease when it is linked, for example, to DNA damage. The generic human heritage, consisting of some 30,000 genes, has been accessible to scientists since 2003 through the development of sequencing techniques (Figure 6.10).

Figure 6.10. Sequencing techniques allow scientists to decode the human genome from the molecular structure of the DNA. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 6.10.– The figure represents a molecular model of the DNA, organized in a double helix. The atoms are represented by colored beads: Carbon in white, oxygen in red, phosphorus in purple and nitrogen in blue (in order to lighten the figure, hydrogen, an atom present in abundance in DNA, is not represented). The background of the image represents the fluorescent bands representing the genes carried by the molecule, as scientists can obtain it from an automatic sequencing machine (source: Peter Artymiuk/Wellcome Collection/www.wellcome collection.org). An emerging discipline, genomic medicine aims to identify certain genetic abnormalities in patients in order to provide them with targeted treatment. It is beginning to transform the way in which disease progression is prevented, diagnosed, treated and prognosed. Sequencing DNA is a health issue with multiple aspects: technical, economic and ethical. High-performance computing means, used in numerical simulation, also serve DNA sequencing techniques, which are undergoing a real revolution and are now bringing genomics into the era of data processing [JOL 17, QUI 17]. For many countries, genomic medicine appears to be a major public health issue because it revolutionizes the development of clinical research, therapeutic management, the care pathway and therefore the organization of public health. In 2016, France was deploying the “France Genomics 2025” plan, which included producing several dozen Po of data per year, including data from DNA sequencing, in order to contribute to the development of genomic medicine. The latter potentially involves all stakeholders in the health field (attending physician, university expert, biological analyst and, of course, the patient himself and his family). NOTE.– Data pave the way for the medicine of the 21st Century. As is becoming the case for many constructions, data analysis is combined with the numerical modeling of different systems: buildings, cars, ships, aircraft and cities. Ambitious to produce a “digital twin” of individuals, these techniques aim, in the field of health, to develop personalized medicine [BAS 14]. Christophe Calvin, IT expert at the CEA, explains: “Digital twins are models ‘in silicio’, i.e. implemented in computers. They make it possible to personalize a patient’s diagnosis and therapy. Genomics, imaging or medical records (reports of visits, operations or interventions): the data concern individuals and allow a digital representation of their state of health. Cross-referenced with statistical data for entire populations, these individual data allow correlations to be established to find a therapeutic strategy.”

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Researchers use these digital representations of human physiology to conduct their studies on diseases, treatments and medical systems. This new tool paves the way for optimizing medical treatments: many medical manufacturers, as well as some regulatory authorities, expect significant innovations in human health that will be promoted by this digital technology. Jean-François Mangin gives an example in neuroscience: “By collecting and cross-referencing data from brain imaging, pathological symptoms and genetic information, data science techniques contribute to the development of early diagnosis tools for brain diseases. Databases of observations made on hundreds of thousands of individuals make it possible to search for genetic, environmental or behavioral factors triggering a degenerative pathology, such as Alzheimer’s disease. It becomes possible to predict its occurrence more than a decade before the first symptoms, which helps to prevent its development.” Data analysis involves many statistical and algorithmic techniques, to which recent advances in artificial intelligence are increasingly contributing. According to Christophe Calvin, these techniques raise new technical and ethical questions for the scientific community: “The data used to make up the ‘digital twins’ are of different kinds. Genomic data is similar to ‘structured’ data, i.e. data that can be coded/decoded. It is supplemented by ‘unstructured’ data, such as those from patient-specific diagnostic or surgical reports, bibliographic data on the pathologies encountered in a population or medical imaging data. Interpreting these data requires algorithms that integrate notions of semantics or efficient image processing in order to extract relevant information. All the tools contributing to this objective are already available to the scientific community. The convergence between high-performance computing and data storage techniques is a major element in this process... to which innovations from the ‘Internet of Things’ may contribute. While the robustness of the learning algorithms based on these data is one of the most important technical issues, the collection and analysis of medical data raises ethical and political questions. Knowledge of the state of health of a population is a security and sovereignty issue for a country, whose citizens must also be protected from commercial or potentially harmful use of their personal data...” Developing “digital twins” is not science fiction and maybe tomorrow these avatars will take treatment before us – but certainly not in our place!

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6.3. Mechanical be ehavior of muscles and organs Modeling the hum man body helpps to understand and heal it. The finitee element Chapter 1 of the first techniquue, particularlly adapted too mechanics in general (C volume), contributes to the deveelopment of models of human h body behavior mplexity lies beyond standardization. The T uniqueneess of the [LUB 155], whose com latter parrtly makes it beautiful b and difficult d to pro opose a mechaanical model.

Figure e 6.11. Finite element e mode el of a leg’s so oft tissue (sourrce: image ow wned by Texise ense and the TIMC-IMAG T la aboratory). For a color versiion of this figu ure, see www.iste.co o.uk/sigrist/sim mulation2.zip

The mathematical m models for mechanical m beh havior of livinng tissues aree complex and the elasticity charracteristics deepend on each h patient: musscles, fats, tenndons and cartilagee react very diifferently wheen external strresses are applied to them. The rigid parts of the body – mainly m the skkeleton – undergo small deeformations, w while the c deform moore significanntly. Dependin ng on the objeectives, the m models are organs can based onn elastic modeels, valid for example e to deescribe bone sttrength, or visscoelastic models, adapted for soft s tissue andd organ deformations. In thhese cases, thhe models q becom mes complex and a expensivee. are nonliinear and theirr calculation quickly In orrder to be usedd in the prepaaration of an operation, o sim mulations mustt give the most acccurate results possible (annd in some situations, withh the shortestt possible calculatiion times). Thheir constraintts are numero ous: in particuular, it is a quuestion of producinng a model thhat can be useed by practitio oners, subjectt to the imperratives of urgency.. Biomechaniccal researcherrs propose sim mulations baseed, on the one hand, on the rapidd generation of o meshes (forr a model speecific to each patient, adaptted to his morphollogy) and, onn the other haand, efficient calculation methods m (closse to real time, alloowing for exaample interactiive simulation ns) [PAY 14]. Whatt solutions are a proposed by mechaniccs to overcom me these diffficulties? Algorithhms capable off quickly prodducing modelss adapted to eaach patient, iddentifying the diffeerent anatomiccal parts (skin surface, bonee, fat, muscless, etc.). By aggregating the imagging data (scannner, MRI) off the body partt concerned, a calculation m model can be produuced in a few minutes. Withh a calculation n tool, it is theen possible too evaluate

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a state of stress in a muscle or part of the body (Figure 6.12), and to anticipate, prevent and heal contact pain, felt when a weakened foot is placed on the ground, for example [LUB 14].

Figure 6.12. Pressure calculated in a foot under pressure on the ground (source: image owned by Texisense and the TIMC-IMAG laboratory). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 6.12.– “Customized models in orthopedics are in some respects more mature than those in cardiac surgery,” comments Édouard Lété. “Requiring comparatively less accurate medical imaging on a fixed organ, it is also not subject to the requirements of urgency. The calculation makes it possible to evaluate the stresses in tissues and cartilage, which give a good picture of the comfort or pain experienced by a patient. Simulation allows practitioners to imagine therapeutic solutions and to anticipate the possible consequences of an intervention.” Each organ of our body has a unique function and interacts in different ways with others at the same time. Mechanical interactions are the simplest, biological or physiological interactions are more complex. Modeling requires a good understanding of these things. Characterizing living organs is thus one of the crucial issues in biomechanics. For example, researchers collaborate to build databases and knowledge relevant to their practice – in particular to select the appropriate behavioral laws for modeling each living organ [PAY 17]. Data are useful for building simulation models, for example to train a gesture on a digital model of a component or on a three-dimensional model, obtained by 3D printing (Figure 6.2). 6.4. Blood circulation In Molière’s century, the English physician William Harvey (1578–1654) discovered the laws of blood circulation and published a summary of his work in 1628 (Figure 6.13).

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Figure 6.13. Excerpt from William Harvey’s book, Exercitatio anatomica de motu cordis et sanguinis in animalibus, Fitzer Publishing, Frankfurt am Main, 1628 (source: www.biusante.parisdescartes.fr)

Based on experimental anatomy, Harvey analyzes the data at his disposal. By studying hearts of all shapes, he measures the average amount of fluid contained in his cavities and the rate of heartbeats. According to his calculations, the heart stirs nearly 250 kg of blood per hour. Set in motion by the heart pump, its circulation takes place within a large network of arteries and veins whose functioning he discovers. The flow of blood through the body is divided into two circuits: – the pulmonary circulation ensures the transport of oxygen and carbon dioxide in the lungs. From the right ventricle of the heart, blood low in O2 and high in CO2 is sent to the lungs via the pulmonary artery. It releases the carbon dioxide and charges itself with oxygen. Then returning to the heart through the pulmonary veins, it arrives in the left atrium and passes through the left ventricle of the heart; – the systemic circulation provides the oxygen necessary for cellular metabolism. From the left ventricle of the heart, blood is sent throughout the body via the aorta and then the arterial system. It then returns to the heart through the venous system, enters the right atrium and is expelled into the right ventricle. Blood is composed of 55% plasma and 45% cells (red blood cells, white blood cells and platelets). Plasma, made up of water and mineral salts, ensures the transport of blood cells, nutrients of food origin (sugars, amino acids, etc.), proteins (hormones, antibodies, etc.) and metabolic waste. Red blood cells are rich in hemoglobin, the protein that can carry oxygen or carbon dioxide, while white blood

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cells are responsible for the body’s defense. Platelets are responsible for blood clotting. Blood rheology is thus complex, but, as a first approximation, the Newtonian fluid model is suitable for simulations in large arteries. However, blood flow models cover a wide range of vessel sizes and characteristic velocities. As we will see in the following sections, low Reynolds numbers occur in microcirculation, while flows in large arteries involve higher Reynolds numbers: the physics of flow is thus very different from one situation to another. 6.4.1. Blood microcapsules Some treatments for cardiovascular diseases, such as myocardial infarction or chronic heart failure, are based on angiogenesis, a therapeutic solution that stimulates the growth of blood vessels. Angiogenesis takes advantage of the targeted diffusion of growth factors that promote the migration and proliferation of vascular cells. In order to optimize the process, the treatment uses microcapsules to ensure the controlled release of substances promoting the angiogenic process. Consisting of a membrane that insulates the contents from the external environment, their very small size allows microcapsules to circulate in the vascular network in order to release their contents [BAN 11]. Numerical simulation helps to size such microcapsules. Anne-Virginie Salsac and her colleagues have developed calculation codes adapted to microfluidic flow conditions. The researcher explains the purpose of the simulations: “As they pass through certain areas of the vascular system, microcapsules can undergo significant deformations. For example, the simulation seeks to ensure that their integrity is not questioned in these situations or that it does not clog the vessels in which they circulate. The flows involved are controlled by a balance between viscous and pressure forces and by strong interactions with membrane deformation.” The numerical simulation, validated by means of dedicated experimental devices, uses a calculation code developed for this class of flows with very low Reynolds numbers. The calculations allow to represent various conditions, close to those encountered in physiological flows and to understand how the capsule is deformed under the effects of the shearing of the blood layers. They provide useful data for selecting membrane materials, their strength or the shape of the capsule to withstand flow conditions (Figures 6.14 and 6.15).

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(b b) Numerical simulation s [SA AR 18]

Figure 6.14. 6 Flow of a microcapsulle (100 large microns) m into a channel of the same size with h sudden wide ening (transitio on to a rectang gular channell [SEV 16] or Y-shaped opening [CHU 13]). For F a color version v of this s figure, see www.iste.co.uk/sigrist/ on2.zip simulatio

Figure 6.15. 6 Numericcal simulation of ellipsoidal microcapsules m s in a single sh hear flow V 11] [DUP 13, DUP 16, VAL

COMMEN NT ON FIGURE E 6.15.– The figure gives examples of the successiv ve shapes taken byy the same elliipsoidal capsuule subjected to a simple shear flow enccountered in the floow of physioloogical fluids such s as plasm ma. Three posssible flow reggimes are observedd, correspondiing to differennt shear rates of flow: rotattion of the cappsule as a solid boddy, transition,, rotation of the t membranee around the capsule in a so-called “tank traack” movemennt. simulation 6.4.2. Angioplasty A Angiioplasty is one of the mostt common tecchniques in noon-invasive suurgery. It consists of restoring thhe failing arteerial circulatio on in a narrow wed vessel by ddilating it

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with an inflatable balloon, introduced endovascularly from one of the vessels passing through the patient’s groin. It may also be accompanied by the installation of a prosthesis, or stent, a metal spring that maintains the distance between the vein or artery to be treated (Figure 6.16).

Figure 6.16. Principle of angioplasty (source: www.123rf.com/ Roberto Biasini)

Numerical simulation is interesting in order to predict the potential success of an intervention: “The simulation is based on a numerical model built from medical imaging data: the patient-specific geometry of the vessel concerned can thus be imported into a calculation code to solve the equations controlling blood flow and vessel deformation. In addition to the construction of a ‘realistic’ geometry, i.e. the one that is most faithful to the patient’s anatomy, the calculation presents two major difficulties: on the one hand, the pulsatility of the flow and, on the other hand, the deformation of the vessels, which locally influences the blood flow. This is a problem of ‘fluid/structure interaction’, also encountered in other industrial problems...” This type of simulation is made possible after a long period of development work, making it possible to have calculation algorithms adapted to the specificities of fluid/structure interaction for biomedical applications (Box 6.1). In order to validate the simulation, researchers are developing dedicated devices, such as a silicone vein model based on imaging data (Figure 6.17).

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Figure 6.17. Experiments on a silicone model allow to validate the simulations [DEC 14]

Its geometric and mechanical characteristics are known with great precision and the calculation can reflect them more easily than on living organisms. The simulation compares flow conditions before and after the intervention (Figure 6.18).

(a) Before angioplasty

(b) After angioplasty Figure 6.18. Numerical simulation of blood flow in an arteriovenous fistula [DEC 14]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 6.18.– The figure shows the blood flow in the arm vessels in a patient with renal failure treated with hemodialysis. To allow treatment and bring the blood to the hemodialysis machine for filtration, access to a high blood flow vein is required. This access was previously achieved by surgically connecting a vein (bottom vessel in the images, where blood flows from right to left) to an artery (top

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vessel where blood flows from left to right). The purpose of numerical simulation is to understand the impact that arterial stenosis, which has appeared on the patient’s artery, has on blood flow rates, pressure and flow, and to test the conditions necessary for the successful treatment of stenosis by angioplasty. Numerical simulation allows different possible scenarios to be tested and helps to find the parameters to restore physiological pressure conditions. In order to be integrated into surgeons’ practice, this type of simulation must show several properties: speed, adaptability and of course precision. NOTE.– Bringing surgeons and simulation experts into dialogue. The validation of simulations is one of the points that guarantees its use in a hospital environment. It may be achieved through collaboration between the different experts contributing to the development of the models. Stéphanie Salmon, professor-researcher at the University of Reims Champagne-Ardenne, explains: “Performing realistic and usable simulations in hospitals requires greater collaboration between simulation experts, who have the knowledge to build models and manage calculations, and surgeons, whose expertise is crucial in interpreting these calculations...” Simulation experts are familiar with flow simulations and can interpret the calculations presented in different ways: visualization of flow lines, intensity of pressure or velocity fields in the blood, stress fields or tissue deformations. Surgeons’ interpretations are based in part on the analysis of medical images. How to ensure dialogue between experts? “We have developed a technique for reconstructing MRI images from digital simulation results, among other things, to give practitioners the opportunity to interpret the calculations. This results in a ‘virtual MRI’, corresponding to the physiological and physical mechanisms represented in the simulation.” The data allow surgeons and simulation experts to understand the phenomena represented by the calculation and to validate the simulation by comparing the actual MRI data with the MRI data reconstructed from the calculation (Figure 6.19). “‘In vivo’ validations remain difficult to implement, measurements on a patient, when possible, pose problems of reliability and reproducibility. The approach we have developed allows us to overcome these limitations and contributes to the dialogue between two disciplines, that of applied mathematics research and that of medicine. The joint construction of digital medicine tools is the best guarantee of their use for the benefit of patients.”

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Figure 6.19 9. Calculation model m and sim mulation of an MRI [FOR 18 8]

COMMENT ON FIGU URE 6.19.– Th he figure on the t left repreesents an initiial threedimenssional mesh of a cerebral venous netwo ork obtained from f MRI acqquisitions on a heealthy subjectt. The figure on o the left is a “virtual MRII image”. It is obtained by processing the reesults of a finiite element ca alculation of blood b flow (in the mesh of the previous figgure) with a sequence off three-dimenssional phase contrast acquisitions. Imagge processing, modeling and a calculatio on techniquess are constanttly being refined so that numeerical simulattion can beco ome a real heelp to practittioners in preparing an operatioon. David Perrrin [PER 15, PER 16], fouunder of PreddiSurge, a French start-up s in the field, explains: “W We have develloped a tool to model an aortic prosthhesis insertionn in patients at risk of an aneuryysm. This prrosthesis is made m of a texxtile wing to deployy the matterial, on whicch are sewn ‘stents’, metal springs allow proosthesis and too apply it on the walls of the t vessel. Sim mulation helpps to dessign this type of o prosthesis and, a in some cases, c to adappt its design too the patient.” The approach encounters e tw wo difficultiees already mentioned ffor other when the applicatiions: the sollution propossed by the simulation iss effective w mechaniical characteriistics of the tisssues and matterials constituuting the prosthesis are well-knoown, and wheen the modelling is adapteed at a lowerr cost to the patient’s morphollogy. “W We worked onn algorithms generating g thee geometry off the model ffrom the imaging datta produced inn the preoperrative phases. The calculaation

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model then created with a finite element method has several thousand degrees of freedom. It is suitable for a ‘static’ calculation to visualize the shape of the prosthesis at the end of the operation. The task is completed in just under a day!” The calculations are carried out using a commercial tool widely used in the industry and allow practitioners to anticipate possible complications in the course of the operation. Three-dimensional imaging data are used to develop a computational model, on which a finite element mesh is based (Figures 6.20).

Figure 6.20. Simulation of stent placement in angioplasty: personalized arterial geometry, CAD model and finite elements and aortic prosthesis placement [PER 15]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

The simulation it facilitates reproduces the main stages of the operation: insertion of the prosthesis into the artery, adaptation to the patient’s geometry, and prediction of the mechanical condition and shape of the treated vessels.

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Researchers and engineers are thus working to develop numerical models of the human body based on algorithms developed for industrial problems (fluid flow, material resistance) and, in return, industrial simulations also benefit from biomechanical research results, as in the case of “fluid–structure interactions” (Boxes 2.2 and 6.1). “One of the many difficulties encountered in numerical simulation in biomechanics is the consideration of fluid/structure interaction phenomena,” explains Jean-Frédéric Gerbeau [GER 05]. Already encountered in transport engineering (Chapter 2), fluid/structure interaction (or FSI) is almost everywhere in biomechanical modeling. The human body involves many flow situations in the presence of deformable material (blood in the vascular system, air in the respiratory system, etc.). To simulate blood flow, biomechanical scientists first tried to use the calculation algorithms developed to meet the needs of aeronautics. This approach quickly met a practical limit, as the algorithms proved to be numerically unstable. It took scientists a few years of research before they could mathematically understand the causes of these instabilities [CAU 05]. “One of the reasons for the instabilities observed in the calculation of fluid/structure interaction in living organisms is the very high proximity of density for the ‘structure’ (e.g. arteries) and ‘fluid’ (e.g. blood) parts. We have shown that the closer the densities are, the more likely the calculation with ‘classical’ algorithms was to be ineffective.” The first stable and effective algorithms for blood flow date from the late 2000s [FER 07, BUR 09]. These methods have made it possible to carry out simulations that were previously unthinkable by dividing the calculation costs by more than 10. The mechanical engineering community currently disposes of algorithms capable of performing close simulations under conditions close to actual biomechanical problems. The stability of the algorithms is such that large deformations of arterial walls due to blood flow can be realistically reproduced in the simulation (Figure 6.21). The stable fluid/structure coupling algorithms respect the mechanical conditions of FSI (equal speeds and continuity of forces at the interface). They generally use two calculation codes, each dedicated to the physics of fluid and solid (Box 2.2). The coupling of digital tools poses certain technical difficulties, and simulations sometimes require long calculation times. The calculation time can be further reduced by using a so-called “monolithic” formulation for the fluid–structure domain, i.e. by solving together the equations of blood flow and vein deformation with a unique mesh size (Figure 6.22).

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Figure 6.21. Coupled fluid/structure simulations in the heart: blood flow rate in the left ventricle (source: INRIA/ REO and M3DISIM project teams). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Figure 6.22. Simulations of blood flow in a right (left) and curved (right) artery using a “monolithic” algorithm [MUR 17b]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

The current applications of this work are nowadays numerous in biomechanics, particularly in cardiovascular surgery, for the design of prostheses, stents or heart valves. Note that, once again, innovation in simulation techniques are often crossing boundaries between applications. Indeeed, the efficient and stable computational algorithms developed for biomedical applications are also well-adapted to the fluid/structure interactions encountered in the maritime and naval fields. Box 6.1. Fluid–structure interaction at the heart of biomechanics

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6.5. Cosmetics The Birth of Venus is one of the most famous paintings by the Italian painter Sandro Botticelli (1445–1510). Venus emerges gracefully, gathered in the conch of a giant shell, rocked by rough seas. Zephyr’s breath carries the goddess’ long blond hair in its wake. Some verses by Charles Baudelaire, taken from a poem from Les fleurs du mal, remind us of this illustrious painting: “Oh curls! Oh, fragrance full of nonchalance! Ecstasy! To populate the dark alcove tonight) Memories sleeping in this hair, I want to shake it in the air like a handkerchief! […] Blue hair, a flag of strained darkness, You give me back the blue of the immense and round sky; On the edges of your twisted strands covered in down I get very drunk from the mixed scents" (La chevelure, [BAU 57], translation from French) Nowadays, beauty products offer to restore the natural reflections of women’s hair, to play with various colors in order to imitate the grace of Venus or to arouse the poet’s delight. Developing cosmetic products that give hair a subtle and longlasting color also requires mathematical techniques. These are based on data that complement equations expressing certain chemical and optical phenomena. Eva Bessac, a researcher at L’Oréal’s R&D center, explains: “Modern hair tints are obtained with the help of dyes. Trapped inside the hair, they absorb some of the light to which they are exposed and restore the desired shade. This mechanism depends, among other things, on the composition of the applied product. Equations describe the phenomena of light absorption and reflection. They involve many parameters that must be characterized, by means of colorimetry tests, carried out on a range of different hair.” A large part of the cosmetics industry’s know-how lies in the use of the best basic components and their mixtures, in proportions that allow a desired color to be obtained. From about 15 dyes, it is possible to create an almost infinite number of colors. Imagining a target coloring, what should be the mixture to be made? This question cannot be answered by systematic testing – even for experts with long experience in this field: it would take too long! Statistical methods allow it: “In order to develop new products or to offer a ‘personalized’ shade, we develop mathematical models to define an optimal mix or to invent new ones with the expected qualities. The approach is based on equations that

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reflect how the product applied to the hair releases light. These equations are supplemented by experimental data specifying the model parameters. These are mixtures of known dyestuffs, produced in different concentrations and applied to hair samples. They are obtained according to a reproducible protocol because their reliability determines the accuracy of the calculation.” With a modeling capable of characterizing all the achievable colors, it is possible to predict which one will be obtained with a given formula! In order to evaluate the effect produced by a shade, experts use established standards. A color may be represented by three sizes: the clarity, and the amount of red and yellow it contains. The mathematical model offers to perform this rating in addition to the sensory evaluations conducted by experts: “We can now correlate sensory evaluations with the rating criteria obtained from mathematical models with great reliability. Modeling allows hair coloring experts to save time, raw materials and unnecessary experimentation. It is a creative tool and does not replace human sensitivity!” The subjective judgment as to the aesthetics of a coloring, whose rendering is a subtle mixture between a color and its reflection, remains essential. In the digital age, Venus still keeps all her secrets. 6.6. Neurosciences Ada Lovelace, a contemporary of Edgar Allan Poe, has turned her own mind into a laboratory: “I hope one day to succeed in equating brain phenomena” (cited in [CHE 17]). She thought mechanically and mathematically about the brain, which in her time was avant-garde because she anticipated certain concepts that are now being developed by neuroscience. Understanding how the brain works – and how it contributes to intelligence – is one of the scientific challenges of our time. While Edgar Allan Poe thought it unlikely at the end of the 19th Century, 21st Century technologies promise it. Researchers can nowadays measure and visualize brain activity. They have different means at their disposal that are used in a complementary way, offering to know the structure of the brain, to understand its activity in different regions and to monitor its evolution over time. This information helps to understand many brain functions [NAC 18]. Complementing these visualizations, some scientists are currently trying to model the brain and simulate its activity. Thus, just as it has become a tool that contributes to other sciences that use it more and more systematically, numerical

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simulation accompanies some brain research. Researchers in neuroscience are developing models that are very similar in principle to those used in the physical sciences. They allow virtual experiments that contribute to understanding the organization of the brain or aim to predict some of its evolution. We have seen that this task remains very difficult (and still beyond the current reach of scientists) for complex physical phenomena, such as turbulence. If it seems much more daring with regard to the brain, it nevertheless becomes a reality. To date, major international projects have set out to provide numerical calculations to simulate, using data and physiological models of brain cells and their connections, the functioning of certain parts of the brain. They are the subject of significant investments in the United States, China, Japan or South Korea, countries with the world’s largest computational resources, and Europe. The European Human Brain Project (HBP2) is one of them. It aims to provide a digital model of the brain, calling for collaboration between researchers from different scientific disciplines (including numerical simulation). It also aims to contribute to the emergence of a computer infrastructure available to researchers in brain sciences and other sciences to conduct part of their research. These are based in particular on techniques for data collection and storage, which contribute to the development of theoretical and numerical models [AMU 16]. Markus Diesmans, a neuroscience researcher and contributor to the BPH project, explains the challenges of simulation: “The brain has a very complex functioning that we are only beginning to understand. It is organized at different levels. The molecules of the matter of which it is made up; the nerve cells, divided into different layers (with a density and variety of cells specific to each species), themselves organized by the proximity allowed by their multiple connections; more global regions, linked to each other. What does this complex, ‘multiscale’ and ‘non-linear’ organization mean? How is it related to brain activity? Simulation in the general sense seeks to know which level of modeling is most appropriate to understand brain function, and aims to reproduce its activity.” For neuroscientists, digital reconstructions and simulations provide new tools for their work3. Scientists use different tools: developed mostly in a collaborative and

2 Available at: http://www.humanbrainproject.eu. 3 Let us add that some scientists even think that numerical simulation, like visualization, may help us to understand the origin of certain brain diseases and prevent their development.

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international context, they are adapted to the description of the brain4. At the level of neurons and their connections, the models represent the electrochemical reactions occurring in these cells, as well as the transmission of information between them. Modeling uses mathematical equations, supplemented by data (such as the type of cells represented in the different neural layers, their density in the areas studied, etc.). Researchers refer to simulation based on both models and data – in this respect, the methodology used is identical to that used by scientists studying, for example, weather or climate (Chapter 4). An example of a detailed simulation of a mouse brain area is provided by Makram et al. [MAK 15]. Like astrophysical models that only take into account a “part of the Universe” in order to be operated (Chapter 3), this simulation is sufficient to perform calculations from which it is possible to extract information. The model is built from a database representing the biological variability observed in the brains of rodents. This describes the anatomical organization of neurons in the brain, their statistical distribution in different areas of the brain and their connections. These are rendered by a random algorithm of neural position and morphology in the studied region. The model represents about 30,000 neurons and nearly 10 million connections between neurons, by axons and dendrites (a total length of 350 m for the former and 215 m for the latter). These connections are expressed by means of an algorithm representing biological rules, the data are supplemented by mathematical equations representing the main electrical and physiological phenomena at work in nerve cells. The brain model is thus described as general. It is not designed to represent a particular type of activity, but rather to perform digital experiments. According to their authors, the simulation validates the ability of a simulation to correctly reproduce certain functions observed in vivo on an animal. It also makes it possible to produce data that is currently inaccessible to experience: “This study demonstrates that it is possible, in principle, to reconstruct an integrated view of the structure and function of neocortical microcircuitry, using sparse, complementary datasets to predict biological parameters that have not been measured experimentally” [MAK 15]. The current limitations of brain simulations are numerous and discussed by the scientific community – to go into detail would go far beyond the scope of this book. Through scientific and ethical debate, researchers build the rationale, limitations and

4 In the toolbox available to scientists, we find in particular models of nerve impulse dynamics and a programming language appropriate to their description. The models, on the other hand, are implemented in different open-source programming codes [GEW 07, PLO 16].

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contributions of digital simulation for their practice [DUD 14, ROS 14]. Markus Diesmans enlightens us on this subject: “The scientific community is developing a wide range of opinions on brain simulations. For some researchers, its use is premature: the knowledge available to scientists today is too limited for calculations to produce exploitable and interpretable results. The structure of the brain is extremely complex and simulations are based on data that do not represent all the scales necessary to reproduce a complete brain. However, the idea of simulating the brain is nowadays relevant to many other researchers. This technique is used pragmatically, becoming a tool accessible to scientists and contributing to their research.” The American author Siri Hustvedt focused on neuroscience for philosophical and intellectual interest [HUS 18a]. She notes this limitation, which other researchers in this field point out with her [DUD 14]: “It is impossible to isolate the brain from what is happening outside it (what we call our environment and our experiences), as well as from other parts of the body that interact with it...” [HUS 18b]. Therefore, a complete simulation of the brain should account for these bodily and environmental interactions, as well as the variability of living organisms. A task that has so far proved impossible to achieve by means of modeling. Markus Diesmans reminds us in a concrete way that the calculation resources called for by complex simulations remain very significant: “Reproducing one second of operating time from a brain area required, for example, nearly 15 minutes of computing time on a supercomputer. The human brain contains just over 85 billion neurons, each with an average of about 10 thousand synapses. It evolves on very different time scales. The plasticity of the brain, its ability to reorganize itself, involves phenomena occurring on extended time scales: from a few minutes to a few months... even years! Fully simulating the dynamics of the human brain is currently beyond the reach of the models and computing machines available to scientists – and therefore remains a very ambitious goal!” Brain sciences nowadays benefit from digital visualization techniques, which will be reinforced by simulation techniques. In both cases, it is worth noting the role played by supercomputers, allowing the processing of large quantities of data or the performance of calculations. Simulation provides new ways for researchers to understand in depth the complexity of the brain, its structure, connections (Figure 6.23) and activity.

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Figure 6.23. 6 Simulattion of the electrical e activ vity of a porttion of a virttual brain consistin ng of seven re econstructionss of neocortica al microcircuitts (source: © The Blue Brain Project/www.bl P luebrain.epfl.cch). For a color c version n of this fig gure, see www.iste e.co.uk/sigrist//simulation2.zzip

Simuulation is not yet y able to offfer the possib bilities of visuualization – w will it ever be? Desppite its currennt limitations, it will most certainly c conttribute to the evolution of the waay some brainn science reseaarch and otherr disciplines are a conducted: “Thhe road to simulation of the t human brrain, or evenn only part off its coggnitive functioons, is long annd uncertain, […] [ but on thhe way, much will be learned. l […] New N methodoologies and tecchniques are also a expected that willl benefit neurroscience at laarge and probaably other scieentific discipllines as well” w [DUD 14]. 1 Artifficial intelligennce might be one of the sccientific fieldss that can bennefit from this reseearch. Presentted as one off the flagship techniques of o the 21st Century, it fascinatees, intrigues and a raises maany questions,, as we have mentioned inn the first volume of this book. For some researchers, thee future of thiis technique llies in its ming AI’s convergeence with otheer disciplines. Thus Geoffreey Hinton thinnks: “Overcom limitation involves building b a briidge between n computer sccience and biology...” A example off this possible connection caan be that (remarkss reported by [SOM 17]). An of neuroo-morphic chiips, of which Timothée Léévi, a researchher in this fieeld [LEV 18], expllains the properties: “Thhese chips aree close to thee energy perfformance of biological b braains, which surpass those t of macchines in term ms of consuumption/execuution speeed. They finnd applicatioons in robotiics and artifficial intelligeence offe fering computtational and learning capaabilities at higher h yields and perrformance thann current calcuulators...”

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Inspired by life, computing systems reproduce the propagation of nerve impulses between neurons: “Some ‘neuro-morphic’ systems are based on deep learning techniques and are designed to automatically develop their connections. These are reinforced when they are requested. This so-called ‘unsupervised’ learning is close to ‘neural plasticity’. The artificial neural networks of which these systems are composed only perform calculations when they are used. They operate efficiently with few IT and energy resources.” Nowadays, several research laboratories and computer companies are announcing the industrial development of such devices, chips and computers [LEO 18, OBE 18]. The structure of the chips on the computers of the future simulates that of the human brain. Will computers be closer to our brains tomorrow?

Figure 6.24. Galway neuro-morphic processor (source: Timothée Lévi, Université de Bordeaux). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

NOTE.– Connected brains? Canadian filmmaker David Cronenberg has made the fusion of human and technology one of the major themes of his science fiction films, questioning the illusion of increasing human performances through technical innovations. Almost 20 years ago, with eXistenZ, he imagined a convergence between human, IT and biotechnology. In the film, humans increase their imaginative abilities by using an organic appendage living in symbiosis with them [CRO 99]. Bringing brains and machines closer together is no longer just a matter of science fiction these days and a lot of research is moving in this direction.

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For example, American researchers claim to be developing an effective technique for stimulating brain activity to overcome certain memory deficiencies [ESS 18]. Other research is aimed at developing electronic components that can be integrated into the brain. The latter could contribute to the collaboration of biological and digital brains – for example, to increase human memory, or to enable them to control computer terminals or even robotic systems. Ordering a robot to assist a disabled person who no longer has the ability to communicate or move is an application being considered. Jean-François Mangin explains that techniques evolve very rapidly, paving the way for major therapeutic innovations: “The next decade will undoubtedly see the implementation of systems to overcome certain handicaps. A chip receiving information from a camera stimulates the neurons involved in image formation in the brain. With deep-learning algorithms, it is planned to extract the information necessary for these neurons in order to generate a realistic image and restore sight to people who have become blind. Similarly, the control of mechanical armor using brain signals from a person paralyzed in all four limbs has become a reality!”

Figure 6.25. Interfering brains and machines: a dream or a nightmare within the reach of 21st Century humans? (source: www.123rf.com/Kittipong Jirasukhanon)

In 2017, Adam Pantanowitz, a South African engineer, said that it is possible to connect the human brain to the Internet. His project entitled Brainternet shows another potential use of EEG:

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“We have developed a device based on a combination of simple elements: a portable electrode headset whose data is processed by a microcomputer and transmitted to the Internet. This device theoretically makes it possible to monitor the electrical activity of a brain in real time and to have access to it via the Web. For several days, two volunteers wore this device and we were able to observe some of their physical activities (such as lifting an arm, distinguishing the left from the right) from a distance, simply by monitoring the transmitted signal...” The experience, recounted by various sites interested in digital techniques [CAU 17 DUB 17, LAY 17], aroused as much interest as rejection, according to its author. The latter wishes to demonstrate the possibilities offered by relatively accessible techniques today and explains their possible use in the medical field: “From our system, we plan to develop an application that would detect abnormal brain activity in patients with epilepsy... and potentially anticipate seizures or assist medical staff.” The engineer also thinks of other uses of his invention: “Using this technique, we can envisage new modes of communication between humans – which would not require passing through language...” He concludes that it is necessary to build an ethical framework to support the development of such techniques. It is an experiment, the first of its kind affirms its author, remaining at a low stage of maturity. Will we be able to literally read minds in the future with visualization and recording techniques? According to the English sociologist Nicolas Rose, we are a long way from that: “Despite what some people say, reading minds using imaging or non-invasive measurement techniques is nowadays science fiction” [ROS 14]. Beyond the anecdote recounted here, let us remember that major technical innovations almost always result from the convergence of discoveries made in different disciplines, as Yuval-Noah Hariri explains about artificial intelligence: “The AI revolution is not only about ever faster computers (and algorithms). It is nourished by advances in the life sciences, as well as in the social sciences” [HAR 18].

7 Individuals and Society

The Industrial Revolution of the 19th Century contributed to the birth of modern advertising. The latter first takes the form of advertisements placed in a newspaper. Marking the entry of a part of the Western world into the consumer era, the term advertising takes on the meaning “of all the means used to make a product, an industrial or commercial company known to the public...”. From the end of the 19th Century, various artists, such as Czech painter Alphonse Mucha (1860–1939) contributed to the creation of advertising images (Figure 7.1).

Figure 7.1. Bières de la Meuse, Alphonse Mucha, advertising poster, 1897, Bibliothèque nationale de France, Paris (source: ©Agence photographique de la Réunion des Musées Nationaux et du Grand Palais)

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Twentieth Century advertising made widespread use of posters and harnessed the power of television to give more weight to advertising campaigns. These gradually occupied a considerable amount of space – to the point of sometimes becoming invasive: “The human eye has never been strained so much in its entire history: it was calculated that between birth and the age of 18, everyone was exposed on average to 350,000 advertisements” [BEI 00]. 7.1. Calculated choices In the 21st Century, business and political marketing was being refined using digital techniques, while becoming an increasingly effective tool – something we have experienced with targeted ads received on the Internet or by other means. The French sociologist Dominique Cardon summarizes the way in which data are used: “Algorithms use the traces of our past to know our future...” [CAR 17]. Combining the study of our numerical traces with a statistical analysis of the data of millions of our peers, these algorithms acquire an effective predictive capability. Who was not surprised by the relevance of some of the suggestions made online by a commercial site? The American journalist Charles Duhhig reports a concrete example [DUH 14]. Based on the statistical processing of consumer data, some data analysts have proposed a model to a supermarket chain that predicts with good reliability the major changes that occur in a household – for example, a future birth. A pregnant woman often unconsciously modifies her food purchases, for example, and the model detects this change. The commercial potential represented by the arrival of a child in a household makes the mother’s pregnancy an ideal period to offer future parents commercial offers by means of discount coupons for all the equipment they cannot do without. The father of a 17-year-old girl, reports Duhhig, was surprised and offended when his daughter received promotional offers that seemed obvious to him by mistake; he complained to the manager of a local store before having a conversation with his daughter and learning more about her hidden life… The “digital traces” are in particular those left by our activity on the Internet [DUL 17]: videos viewed on YouTube, Google queries, purchases on Amazon, likes on Facebook to name only the most obvious. And these traces can help to build human behavior patterns useful for understanding their preferences, habits, personality and how they achieve certain choices (political, economic, etc.): “Our findings highlight that people’s personality can be predicted automatically and without involving human social-cognitive skills […] The potential growth in both the sophistication of the computer models

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and the amount of the digital footprint might lead to computer models outperforming humans even more decisively” [YOU 15]. From the most innocuous to the most fundamental, our lives – and those of the community to which we belong – are made up of choices. According to Yuval Noha Harari, in their sometimes rational appearance, our choices are fundamentally guided by our feelings: “Ninety-nine percent of the decisions we make, including the most important choices about our spouse, our career and our home, are the result of refined algorithms that we call sensations, emotions and desires” [HAR 16]. Harari thus suggests that our feelings are in reality only calculations, and can therefore be accomplished by algorithms that will eventually become “better advice than our feelings...” [HAR 18]. As the Cold War divided the world into two camps, the American mathematician John Nash (Figure 7.2) became theoretically interested in the conditions that might or might not lead humans to cooperate.

Figure 7.2. John Nash (1928–2015)

COMMENT ON FIGURE 7.2.– John Nash’s work is considered one of the most brilliant intellectual contributions of the 20th Century: it has many applications in economics and many fields of mathematics, such as the study of partial differential equations. Part of Nash’s story is told in the film A Beautiful Mind [HOW 01]. Australian actor Russell Crowe plays the role of the mathematician and makes himself the

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medium of one of his obsessions: to put in equation a real win–win relationship between human beings, a formula that guarantees more harmony. In 1951, he published the results of his reflections on non-cooperative games, giving a formal framework to the interest of players in making an optimal choice for them, while not knowing the choice of an opponent. These studies have applications in economics: they help to explain competitive or cooperative strategies. The prisoners’ dilemma illustrates, while simplifying, part of his thinking. A crime has been committed and two suspects, let us call them Faye and Warren, are being arrested by the police, but they have no evidence to charge them. When questioned separately, Faye and Warren are proposed the following offer by the investigators: “If you report your accomplice and he or she does not report you, you will be released and the other will be sentenced to ten months in prison. If you denounce him or her, you will both serve five months in prison. If no one denounces himself or herself, this penalty will be one month in prison for both.” An analysis of this offer can be made in terms of gains/losses. It shows that the proposal is not zero-sum: there is a dilemma because the temptation (to denounce) offers an immediate reward that is stronger than cooperation. Faye can....

Warren makes the decision to....

...remain silent

...denounce Warren

...remain silent

−1/−1

10/0

...denounce Faye

0/10

−5/−5

Table 7.1. A version of the prisoners’ dilemma

Thus, based on a rational analysis, Faye and Warren are led to say to themselves: “Whatever the other’s choice, it is my interest to denounce him/her.” They will probably realize it, whereas this choice is not optimal: by cooperating (by keeping quiet) they both get away with it, with less pain. It should be noted that, in reality, Faye (Dunaway) and Warren (Beatty) do collaborate, for our greatest cinematic pleasure, by bringing Bonnie and Clyde to life [PEN 67]. The choice to cooperate can only arise from a reflection that brings out the common interest and from a trust in each other. This model, which some use to justify an organization of the economic world such as everyone’s war against everyone (and explain the tendency not to cooperate), can also be valuable in giving

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substance to the win–win option that can emerge from an external analysis of the situation. The prisoners’ dilemma suggests that optimal collective choice is possible beyond the optimal of each other – in other words that cooperation is perhaps also the profound nature of the living [DIA 12, SER 17b, WRI 99]. Understanding individuals or societies using data helps to predict individual or collective choices. Collective investment policy, enterprise development strategy, evaluation of public services, development of commercial offers, operation of networks and infrastructures, regulation of community life: the uses of these models are varied. Based on the knowledge of individuals, made possible by statistical analysis and other means, they contribute to decision-making for the benefit of communities, companies, associations and their respective members. This chapter provides some examples of models that can be applied to certain social issues or contribute to personal or collective decision-making1. 7.2. A question of style Created in 1892 by the will of the French writer Edmond Goncourt (1822–1896), the literary prize bearing his name is awarded every year in France. Since its first award in 1902 to French-speaking authors, it has helped to promote many writers and major literary works. In 1956, the French writer Romain Gary (1914–1980) received this award for his work Les racines du ciel [GAR 56], and a few years later in 1975, the jurors of the Goncourt Academy awarded the same prize to an unknown author, Émile Ajar, for his novel La vie devant soi [AJA 75]. After Gary’s death, we discover that Ajar was a pseudonym he used to publish other novels and try to renew his style. Organized by the writer with the complicity of his cousin, this literary deception makes Gary the only novelist to have received the Goncourt Prize twice. Publishing about 20 works under his name and almost as many under the

1 Some examples testify to the current power of algorithms, and allow us to glimpse their future capabilities, which we can imagine for various uses. While our century is witnessing the concrete achievements of these algorithms, some thinkers seem to have anticipated their possible drifts. Thus the French philosopher Simone Weil (1909--1943) estimated, in the last century, that “(money,) machinism (and) algebra (would be) the three monsters of the present civilization” [WEI 47]. Also making possible the large-scale surveillance of citizens and societies for the benefit of public or private interests [LAR 18] or the advent of a world governed by algorithms for the benefit of a minority of humans [DUG 16], some of their uses can help to embody the Orwellian nightmare [ORW 49]. As our purpose here is not to address this dimension, we suggest that the reader completes his reflection with the authors exploring it in depth [CAR 14, CAR 16, HAR 17, HAR 16, HARA 18, SAD 13, SAD 15, SAD 18].

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pseudonym Ajar, Romain Gary poses an enigma to literary specialists: is it possible for an author to adopt two different styles, to develop two independent literary works and not to be unmasked? Romain Gary himself seems to doubt it. The French researcher Dominique Labbé, specialist in semantic analysis, reports these words from the writer: “I don’t think there is any possibility of ‘duplication’. The roots of the works are too deep, and their ramifications, when they appear varied and very different from each other, cannot withstand a real examination and what was once called ‘the analysis of texts’...” [GAR 81]. The analysis Gary refers to is the art of literature connoisseurs: the texts and context of a work, style and life of an author are part of their reading grid. At a time when Gary/Ajar were publishing their works, other study tools are also available: “By the late 1970s, computers already had respectable power and the intellectual tools necessary to ‘unmask’ Ajar were potentially available. Yet no one has thought of using ‘lexical statistics’ to solve this enigma, including researchers” [LAB 08]. Lexical statistics are based on different tools, one of which is the observation of certain characteristic combinations of words. The analysis of the most frequent “repeated phrases” is, from the point of view of author attribution issues, one of the most effective ways: “A phrase is a stable combination of several terms that each individual chooses in a privileged way and that indicates a certain relationship to oneself, to others and to things. The subject may view these relationships in terms of action (e.g. ‘doing’, ‘going’, ‘saying’), possibility (e.g. ‘enabling’, ‘allowing’, ‘letting’), will (e.g. ‘choosing’, ‘deciding’, ‘wanting’), moral or legal obligation (e.g. ‘duty’), imperative (e.g. ‘must’), knowledge (e.g. ‘experiencing’, ‘knowing’, ‘learning’).” A dedicated algorithm allows these combinations to be found in written texts: the frequency of phrases is therefore a trace of an author’s style. The analysis of nine novels by Gary/Ajar shows their stylistic proximity according to this criterion (Table 7.2).

Individuals and Society

Texts signed by Emil Ajar

Texts signed by Romain Gary

means 7.20

means 5.80

be able to be 4.90

be able to be 3.62

be able to do 4.40

be able to do 2.97

have to be 3.10

to be 2.39

go for 2.90

to go to the 2.20

to be able to live 2,70

to have 2.13

drop out 2.30

to be able to say 2.13

to have 2,10

drop out 1.87

go see 2,00

let go 1.55

to have to do 1.80

push 1.49

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Table 7.2. “Repeated phrases” in four works by Émile Ajar and five by Romain Gary [LAB 08]

COMMENT ON TABLE 7.2.– The table presents the first 10 “repeated phrases”, as identified by an algorithm, in works by Émile Ajar and Romain Gary. Considering only the first 20 combinations, Dominique Labbé, who carried out the analysis, finds that the texts signed Gary and Ajar share 13 of them, the first five being in the same hierarchical order and with practically the same relative frequencies. Given the immense diversity of possible word combinations, it is very unlikely, if not impossible, to encounter two individuals with the same preferences for several specific combinations, in approximately the same order and with similar densities. According to the researcher, this analysis therefore makes it possible to show that Romain Gary is indeed the author who hides behind the pseudonym of Émile Ajar! However, he adds: “For the time being, almost all researchers are convinced that computers cannot help to recognize the author of a single text; a fortiori the genre or personality of its author is out of reach.” In the 21st Century, data processing algorithms were reaching an efficiency and precision that allowed some researchers to extend this analytical work, in order to attribute a work to an author, to understand the style of a great master of painting, or even to perform an automatic personality analysis. 7.2.1. Assigning a work to its author John Lennon (1940–1980) and Paul McCartney (1942–), who together wrote most of the Beatles’ songs, bequeathed to popular culture some of the most famous musical compositions of the last century. Everyone can associate an emotion or a

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memory with one of the Fab Fourr’s pieces, wh hose lyrics annd/or melody, although a McCartneey, are actuallly designed byy one or the oother. For attributed to Lennon and some coonnoisseurs off their music or lovers off their texts, attributing the first or second to t its author reemains a mattter of precisio on, or a matterr of justice! Inn My Life (Figure 7.3) 7 is, for exxample, one of the Beatles’’ songs for whhich there is sstill some doubt abbout this attribbution.

Figure 7.3. First measure of music m of In My Life (represen nted as a tabla ature for guitar)

COMMEN NT ON FIGURE E 7.3.– Ranked d 23rd in 200 03 in Rolling Stones magazzine’s list of the 5000 greatest soongs, In My Life L was relea ased by the Beeatles on Deccember 3, 1965 on the Rubber Soul S album. It I has been taken up by maany performerrs of very ash (1932–20003) being unddoubtedly differentt styles – that of the Americcan Johnny Ca one of thhe most poignnant. In this song, s John Leennon evokes a search for lost time, recallingg those he meet, in which places, p underr which circuumstances: “T There are places I’ll remember // All my life, though somee have changeed // Some forrever, not for better // Some have gone and soome remain // All these placces have their moments me are dead annd some are liiving // In // With loovers and frieends I still cann recall // Som my life, I’ve loved theem all”. A paassage to the piano, of barroque inspiraation, was B prodducer. It contrributes to arrangedd by George Martin (19266–2016), the Beatles’ the nostaalgic atmosphhere of the pieece. In My Life L is one of the very few ssongs for which thhe level of coollaboration between b John n Lennon andd Paul McCarrtney has been dispputed since thhe Beatles spliit in 1970. In 20018, three Norrth American researchers used u data analysis techniquees to find in the songs by Lennnon and McCartney characteristics off each other’ss musical T use technniques similarr to those of leexical analysiss, as mentioneed above, styles. They applied to t the musicall context:

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“For Lennon-McCartney songs of known and unknown authorship written and recorded over the period 1962–1966, we constructed five different bags-of-words representations of each song or song portion: unigrams of melodic notes, unigrams of chords, bigrams of melodic note pairs, bigrams of chord changes, and four-note melody contours. We developed a (statistical) model for dependent bags-ofwords representations for classification. The model assumes correlated multinomial counts for the bags-of-words as a function of authorship. Out-of-sample classification accuracy for songs with known authorship was 80%. We demonstrate the results to songs during the study period with unknown authorship” [GLI 18]. In a conference dedicated to statistical analysis, they present the results of a study that allows them to attribute with certainty the authorship of the melody of In My Life to John Lennon. 7.2.2. Understanding a pictorial technique With regard to the French painter Edgar Degas (1834–1917), Paul Valery wrote these notes on the painter’s work (they can be found in his notebooks where handwritten texts are combined with sketches and mathematical formulas): “A work for Degas is the result of an indefinite amount of studies; and then a series of operations. I believe that he believed that a work can never be ‘completed’” [Exhibition “Degas, Danse, Dessin”, Musée d’Orsay, Paris, November 28, 2017–February 25, 2018]. For most of his paintings, Degas carried out a large number of drawn studies; rendering of expressions, draperies, light, poses, details: data prior to the production of a work. An approach and work shared by many artists, and by digital engineers. Graphic techniques, such as painting, may be reproduced today by simulation. In 2016, a team of researchers, computer scientists and art specialists from the University of Delft, thus carried out an experiment presented as unique and spectacular: that of entrusting an algorithm with the task of creating an unpublished work, inspired by the Dutch painter Rembrandt van Rijn (1606–1669), master of the chiaroscuro technique. Based on detailed data on Rembrandt’s paintings (subjects, shape of facial elements, lighting, materials used – canvases and pigments), a master’s style painting was designed using algorithms for data acquisition, analysis and management, learning and 3D printing techniques. The project is told by its authors on the website www.thenextrembrandt.com. No robot or computer with

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extraordinary capabilities has shown creativity and sensitivity, in the sense that we can understand it for a human artist, to create this painting (Figure 7.4).

Figure 7.4. The Next Rembrandt, a table designed with digital techniques (source: www.thenextrembrandt.com)

Everyone will be able to compare The Next Rembrandt with the original works that inspired the machine and the humans who programmed it – such as The Union of the Drapery Guild (1662) – and get an idea of its aesthetic quality. Let us read how the authors of the experiment proceeded by imitating Rembrandt’s style using the computer: “To master his style, we designed a software system that could understand Rembrandt based on his use of geometry, composition, and painting materials. A facial recognition algorithm identified and classified the most typical geometric patterns used by Rembrandt to paint human features. It then used the learned principles to replicate the style and generate new facial features for our painting” [www.thenextrembrandt. com]. The techniques developed in this project make it possible to understand the style of a painter, this mixture of technique and sensitivity explaining his singularity, by means of experiments allowed by a numerical simulation. We can also to some extent look at this project as a numerical experiment based on information other than equations: on data. It shows that numerical simulation is based on other techniques and testifies to the power offered by those of algorithmic learning, implemented for

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example with specific techniques by programs that have been able to beat humans at different games (Chapter 4 of the first volume) and shape recognition [BLA 17]. 7.2.3. Discovering a personality type The description of human personality and the study of human behavior may also be old – and in some respects more complex – than mathematics. In a text that has been the work of a lifetime, the French moralist Jean de La Bruyère (1645–1696) offers written portraits of his contemporaries, those of the century of Louis XIV. He thus distinguishes among his fellow human beings supposedly universal archetypes [BRU 88]. The ambition to map characters and tell the story of human comedy is constantly renewed by literature, cinema and, in the 21st Century, by television series. Psychology develops models based on a classification into central character traits that provide a benchmark for the theoretical study of personality. Some psychologists consider that five factors would be sufficient to describe it, using the so-called “OCEAN model” [GOL 93], which some researchers use, for example, to simulate crowd behavior [ALL 08]. According to this model, the dimensions of personality are “Openness” (marked by imagination, intellectual curiosity and the desire for new experiences), “Consciousness” (corresponding to the need for success and involvement in work), “Extroversion” (expressed as a tendency to externalize or act), “Agreeableness” (observed in the willingness to help and trust others) and “Neuroticism” (characterized by emotional instability and a tendency to anxiety or irritability, for example). As a result of observation, the OCEAN model is based, among other things, on a statistical analysis of the vocabulary that participants in behavioral studies use to talk about themselves or others – as the French poet René Char (1907–1988) put it: “The words that will emerge know about us things that we do not know about them” [CHA 77]. Do algorithms know how to discover it better than we do [BACK 18, YAR 10]? If the answer remains difficult to state with certainty today, some researchers are convinced of it: “Recent developments in machine learning and statistics show that computer models are also capable of making valid personality judgements by using digital records of human behavior” [YOU 15]. The approach of establishing character traits, which is partly revealed by semantics, aims to describe the characteristics of an individual and to predict his or her behavior in certain situations. It is used for research purposes in behavioral psychology and is used in other fields of the social sciences. Personality models are among the rational elements of a broader theory of mind. They are a tool that psychologists can use, for healing purposes, in a supportive and collaborative

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relationship. They are also used for other objectives, such as marketing and recruitment. Thus, some are based on presented algorithms that are able to grasp the meaning of a text. Let us illustrate our point with a concrete example: an improved version of the personality tests offered by various magazines or online sites. Based on a written document (text, letter, blog article, or even speech or interview), an application developed by IBM aims to define individuals’ personality traits (and their probable corresponding commercial behavior). It provides a systematic analysis based on algorithmic learning techniques. It is able to analyze the implicit content of a text in human language using criteria from the OCEAN model. This way of drawing psychological profiles is in some respects crude and incomplete. Our personality and behavior are indeed complex and are as much the result of our intimate nature, our education, as they are of our life experiences – a set of factors that a model or algorithm cannot yet fully account for. However, some psychological studies suggest its relevance and social science researchers argue that the model is robust enough to be used for predictive purposes, for example, in marketing or human resources, to assess client satisfaction or to develop a personality profile of a candidate for a position [ADA 18, ANA 18, MAC 18, REN 12]. Thus, this type of modeling is implemented using analytical tools to which data processing techniques give a new dimension2. Let us do an experiment with Martin Luther King’s well-known text, I Have a Dream. In just a few seconds, the application produces a personality synthesis in these terms and provides a visual analysis (Figure 7.5). Despite its stereotypical nature, we can find in this description personality traits that are consistent with the overall image we have of a man like Martin Luther King3.

2 It should be noted that the requirements of marketing are not those of medicine or engineering, for example, areas in which high predictive reliability is expected, whereas in mass marketing, the quantity of profiles analyzed can somehow compensate for the quality and effectiveness of the purchase suggestion. 3 The pastor of Montgomery, engaged in a political struggle for civil rights in the United States in the 1960s, is a public and historical personality whose words, world view, thoughts and actions are generally known (non-violence, altruism and compassion, political and spiritual commitment, intellectual courage and curiosity, political voluntarism and militant action, etc.). We use his text for the purpose of the demonstration, hoping to learn no more than we already knew. The way some historians view his personality and action is still the surest way to get to know both. Note that the analysis algorithm does not recognize the speech delivered by Martin Luther King, nor its author, what another program (or a human!) would be able to achieve. We can also ask ourselves how he would have been able to analyze a text as rich, imaginative and intriguing as James Joyce's Ulysses [JOY 22].

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Figure 7.5. An automatic analysis of personality traits. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 7.5.– This graphical representation of an automated personality analysis is obtained with the Personality Insight application, developed by IBM (source: https://personality-insights-demo.ng.bluemix.net). It is based on the analysis of the speech delivered by Martin Luther King in 1963, in Washington (source: http://lesgrandsdiscours.arte.tv). The analysis is supplemented with the following comment, automatically derived by the application: “You are analytical, restrained and guarded. You are appreciative of art: you enjoy beauty and seek out creative experiences. You are empathetic: you feel what others feel and are compassionate towards them. And you are philosophical: you are open to and

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intrigued by new ideas and love to explore them. Your choices are driven by a desire for discovery. You are relatively unconcerned with both achieving success and taking pleasure in life. You make decisions with little regard for how they show off your talents. And you prefer activities with a purpose greater than just personal enjoyment. You are likely to like historical movies, volunteer for social causes, like classical music. You are unlikely to be influenced by social media during product purchases, prefer style when buying clothes, be influenced by brand name when making product purchases” (https://personality-insights-demo.ng.bluemix.net). Let us remember beyond the anecdote that analysis is produced on the basis of a text and that its only purpose is to draw broad personality lines, which is the objective sought. The tool benefits from different contributions in the social sciences (linguistics, psychology, etc.), coupled with the analysis of massive data. Like psychoanalysts who are interested in the words we use and the associations of ideas they suggest, these algorithms wish to correlate our words with other data and discover aspects of our personality – some of which we would ignore. NOTE.– The unconscious within reach of algorithms. Recognizing a literary, graphic or musical style – and the personality that created it – becomes within reach of statistical and computer analysis. Having numerical models that predict personality traits and behaviors could change many human practices [HIR 12]. This is already the case in some areas such as human resources (personality analysis of a candidate during recruitment), sales and commerce (analysis of a potential customer’s consumption habits), and online dating sites (analysis of the psychological compatibility of subscribers). According to their designers, many models are becoming so reliable that the judgment capacity of algorithms will exceed that of humans to describe (and predict) some of our life choices. What other possible uses? For what other purposes? Could they contribute to a questionable standardization of personalities and behaviors – with consequences for individual and collective freedoms? A website can, for example, offer a sale price adapted to our psychological profile, or to other data, such as our income, our place of residence – or even more personal information – with all the deviations that this allows. For example, a sale price can be set according to membership of a social, ethnic, religious or other category or according to a state of health. In the extreme, it can be individualized according to inexplicable criteria. With the processing of our data, we are entering into a possible new form of discrimination against human beings. Discrimination that would no longer be collective (that of belonging to a given group), but individual [HARA 18].

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Do alggorithms allow w us to learn more m about ou urselves? Frennch computer scientists Serge Abiteboul A andd Gilles Dow wek seem to affirm a in Renéé Char’s lineaage: “Our unconsscious is withhin reach of algorithms... as our collecctive unconsccious that remainns to be explorred” [ABI 17]. A searcch engine gathhers valuable data in this arrea. With nearly 90% of the world’s uses, Google G proceesses more thhan 3 billion queries per day. d From thhese data, algorithhms are ablee to learn a lot l about Inteernet users. Im maging GooggleTrends statisticcs, Americann artist and graphic g designer David MacCandles M shhows the evolutiion of the num mber of searcches associateed with the keywords k #Sexx, #Porn, #Weathher, #Wikipedia, #Love, #Food # and oth hers, betweenn 2004 and 22009. Not surprissingly, #Sex caracoles in the lead, joiined by #Porrn... and folllowed by #Weathher, then #Wiikipedia. Thosse who are lo ooking for a liittle sweetnesss can rest assuredd: #Love is fifth on this list! And #G God? He rem mains stable, in eighth positioon, behind #Caars and... #Obbama [MAC 14 4].

Figure e 7.6. Hierarch hy of keyworrds #Sex (blue e), #Weather (red), #Love (yellow), #Food (green) and #God # (purple)) in Google se earches from 2004 to 2018 8 (source: https:///trends.google e.com/) For a color version n of this figure e, see www.isste.co.uk/ sigrist/s /simulation2.ziip

“Everyyone lies. Lyiing well, that’s what it tak kes” makes thhe French novvelist and philosoopher Albert Camus C (1913––1960) say to one of his ficctional characcters, who is nevvertheless in love with virtue v [CAM M 50]. Nowadays, Seth S StephensDavidoowitz, an Ameerican data sccientist, says nothing n else about a humans – and he furtherrmore states itt is impossiblee for them to lie to Big Dataa [STE 18]: “Evverybody lies […] People lie l to friends. They lie to boosses. They liie to kidds. They lie too parents. [… …] And they damn d sure liee to surveys. […]

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How w, therefore, can we learn what our fellow humans are a really thinkking andd doing? Big data. Certainn online sourcces get peoplee to admit thiings theyy would nott admit anyw where else. They T serve as a digital ttruth seruum…” [STE 17a]. Let us ask the search engine a quuestion. It spontaneously offfers suggestioons based d indicates thaat they are preedictions. on the most extensivve research froom others, and a individuall, provide Its proposals, reflectting previous requests, botth collective and m statisticaally numerouss research, annd in some caases may indicattions of the most have suurprises that everyone cann comment on n – they couldd also be of innterest to researcchers in the soocial sciencess and humanitties (Figure 7..7). The conteent of our researcch says a lott, at the sociietal level – in this case, the United States in Stepheens-Davidowittz’s study [STE 17b] – about a the anxxieties, prejuddices and stereottypes that mosst of us work with. w

Figu ure 7.7. Which h word is statisstically more liikely to compllete a Google search starrting with “Is my m husband...””? What can we w learn from queries q on a ssearch engine [STE 17 7a]?

We alsso know that the t informatioon presented by b the search engine e in respponse to a requestt is not insignnificant: the allgorithm choo oses for us thee hierarchy off the data made available to us based onn what it alrready knows about us. F For some i a cognitivee bubble by thhis means. Ass a result, socioloogists, we maay be locked in we aree less often confronted c w with ways of thinking that differ from our own

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through our research on the Internet. This raises serious questions about our freedom, our curiosity and the diversity of points of view that are useful in the exercise of political choices [AGO 18, CAD 16], as the American lawyer Lawrence Lessig [LES 00] points out: “We have moved from common platforms to increasingly fragmented platforms, which produce a world in which everyone lives in their own information bubble. [...] We do not know how to build a space in which people could discuss the same political issues, based on a common framework and a shared understanding of the facts [...] – because of the algorithms and architecture of the network” (remarks reported by [GUI 16]). The Internet provides us with a wealth of information and data whose easy access has no equivalent in human history. A search engine develops a form of intelligence marked by its ability to link data. Does this technique make us smarter in return? Does it awaken our critical sense, develop our capacity for analysis, reflection... concentration? Our use of digital techniques also depends on us and in the face of “algorithmic intelligence”, it is up to us to adapt: “Algorithms take very deep traces in our personal lives and this is a real problem, but users have resources: using ad blockers, other search engines than (the only) Google. You have to enter into this learning loop to have a strategic relationship with the world that falls on you...” [CAR 16] Thus, if there is a risk of seeing the algorithms used to know our behaviors and influence them, we nevertheless retain a real margin of maneuver through our choices [ABI 17]. 7.3. The shape of a city “The shape of a city changes faster, as we know, than the hearts of mortals”: it is with these words, borrowed from Charles Baudelaire, that the French writer Julien Gracq (1910–2007) begins words in a novel in which he explores his residential school years in the city of Nantes [GRA 85]. He finds in his memories the material of the imagination from which he explores the reality of an urban realm. A mentally reconstructed portrait of a city and its inhabitants whose activities he observes and comments on. Twenty years after Gracq, children created a subjective map of Nantes that proposed their perception of the city (Figure 7.8).

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Figure 7.8. Subjectivve map of the city c of Nantes (source: ww.geographiiesubjective.orrg). For a colo or version http://ww of this figure, see ww ww.iste.co.uk/s /sigrist/simulattion2.zip

7.3.1. Transport T Urbaan areas are changing c as a result of inv vestments maade by compaanies and communnities, the behaavior of userss of networks and means off transport, innnovations from ressearch or induustry. The soccial and environmental chaallenges, as w well as the technical challenges of o new urban mobility m will sculpt the shaape of a city inn the 21st fic flows, econnomic or heallth statistics, quality of lifee at work Century.. How? Traffi and useer testimoniess all contribuute to analyzzing the moobility choicees of the inhabitannts of a territtory. The dataa allow a diag gnosis to be made m of roadd network congestion and help to propose soolutions that can be appliied at differennt scales. o smartphon nes indicatingg traffic condditions to From thhe applicationn available on investmeent decisions contributing c too spatial plann ning, their usees are varied. Innovvations in traansport are riising (shared car service): simulation makes it possible,, for example,, to simulate thhe impact of a new decisionn or offer befoore testing it in the field. Reza Vosooghi, V reseearcher at IRT T System-X inn the field of mobility, explains the principless: “Soome simulatioons concerningg urban transp port are basedd on ‘multi-aggent’ models. This is the most reccent approach h applied in this field and is uch as Robot--Taxi, on-dem mand suittable for studyying new travvel services, su or shared mobility services. These simulaations require detailed dataa on o socio-professsional) and on o the urban aareas travvelers (socioddemographic or studdied (mapping of roads, trransport netwo orks or cycle paths, etc.). The

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information used by such a simulation in France has various origins. In France, they come from INSEE, the ‘Enquête Ménage Déplacement’ (EMD), or the ‘Mode d’Occupation du Sol’ (MOS). The simulation is based on an ‘artificial population’ whose activities (work, leisure, etc.) are reported as accurately as possible...” The simulation represents modes of travel and trips associated with activities performed by each agent during the day (Figure 7.9). It is based on an algorithm that iteratively seeks to satisfy the mobility needs of all modeled agents over a given period of time. “For example, we carried out a complete simulation of the Île de France transport network. With 12 million agents represented, which is the actual population of this region, the simulation requires nearly a month of calculation! Reducing computation times is a global challenge for the simulation of large cities and part of our research work consists in developing more efficient methods... Many simulations nowadays use an open source tool, developed in a collaborative way by researchers interested in transport or logistics. The cumulative contributions of each of them to the development of the tool represent more than 30 years of work!”

Figure 7.9. Mobility simulation in the defense district. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 7.9.– The model is implemented with the so-called MATSim simulation tool. It makes it possible to visualize the likely mobility choices of a group of inhabitants. The colored dots represent an artificial population, classified into different socioprofessional categories: employed or not, male or female, staying at home or not, student, etc. (source: Reza Vosooghi, IRT System-X).

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With the data, researchers can evaluate the choices of users of new vehicle services [VOS 19] or anticipate changes in transport networks and means, in order to make large urban areas a shared and peaceful space. A shape of the city in which the human being is the center? Researchers working on shared mobility modes are heading toward this goal. Develop transport solutions that help reduce the number of vehicles in the city and the energy required to build and use them. 7.3.2. Sound atmosphere In his novel, Julien Gracq recalls his first encounter with the city of Nantes. His perceptions have left an indelible mark on him and the writer refers in particular to the city’s sound atmosphere, made up of acoustic traces of human activities: “This was during the years of the 1914-18 war; the tramway, the soap factory, the glorious, majestic parade of the train through the streets, which seemed to miss only the hurdle of acclaim, are the first memory I kept of Nantes. If there is a darker shade at intervals, it is due to the height of the buildings, the surrounding streets, which surprised me; in total, what is left over from this fleeting contact is – rising from its sound, shady and watered streets, from the joy of their agitation, from the crowded coffee terraces of summer, refreshed like a mist by the smell of lemon, strawberry and grenadine, breathed in as you pass by, in this city where the diapason of life was no longer the same, and since then, unforgettable – an unknown, unusual and modern perfume” [GRA 85]. The noise environment is nowadays the focus of public authorities and citizens, in particular because of the health consequences of noise to which city dwellers or people living near industrial installations (airports, stations, factories, wind turbines, etc.) are exposed. Cognitive loss, sleep disorders, stress, cardiovascular risks, etc. Noise conditions our quality of life and in some cases, it can cause extreme suffering. In France, for example, the societal cost of noise pollution is estimated at more than 57 billion euros per year [EY 16], including more than 16 billion for the Île de France. A regulatory corpus is being developed to anticipate risks, protect and inform citizens exposed to noise. For example, a European directive covers the assessment and management of environmental noise: “As a complement to the abundant Community legislation on noise sources, the European Directive 2002/49/EC, promulgated on 25 June 2002 in the Environment Code, specifies, for large urban areas and major transport infrastructures, the production of so-called ‘strategic’ noise maps. The directive aims to establish a harmonized assessment, in the

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25 European Staates, of enviroonmental noisse exposure byy means of nnoise nt and reducee excessive nnoise mapps. This directive also heelps to preven throough action plans, proteect quiet areas and enssure that puublic infoormation andd participation are at the heart of o the process” [ww ww.bruit.fr]. Noise maps (Figurre 7.10) are thhus drawn up for Europeann cities with m more than u numerical simulationss based on phhysical modells and the 100,000 inhabitants using use of ennvironmental data (built, grround, road traaffic, industriaal, air traffic, eetc.). The latter connstitute the innput data of thhese models an nd are subjectt to some unceertainties, which are not withouut consequencce on the asssessment of the t simulationn results, o usingg engineering software. s mostly operated

Figure e 7.10. Road noise n map of the t city of Nan ntes (source: IFSTTAR/CER I REMA). Forr a color versio on of this figurre, see www.is ste.co.uk/sigriist/simulation2 2.zip

COMMEN NT ON FIGURE E 7.10.– Noise maps, available on the Inte ernet, are diaggnoses of the noisee exposure off populations over o a wide area a for a given noise sourrce (road, rail, inddustrial or aiir noise). Freench regulatio ons provide for f noise maaps to be producedd according to the types of sources and a periods of o the day, w with noise thresholdds translated into quantitaative terms. The T road noiise map of thhe city of Nantes presented p herre is obtainedd with “simpllified modelinng”. The coveered area represennts 65 million m2, it containns 1.7 million n calculation points p and 3446 million source points. p The sim mulation is obttained in just above 1 hour of calculationn.

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Benoît Gauvreau and Gwenaël Guillaume, researchers in environmental acoustics at IFSTTAR* and CERAMA* [GAU 15, GUI 09], explain the stakes of the calculations: “Acoustic simulations are based on three main elements: knowledge and characterization of sound sources, sound wave propagation models and criteria for analyzing calculation results (indicators, maps). Human and animal activities (conversations, songs, etc.), transport (cars, trams, subways, planes, etc.) or industrial installations (factories, wind turbines, heat pumps, etc.): there are many sources of noise in the environment. Each has its own characteristics, in terms of duration, level, stationarity or directivity, and covers a certain frequency range. The accessible data make it possible to model more or less accurately some of the various noise sources present in our environment (road, rail, air, industrial traffic).” The propagation of sound waves obeys multiple physical mechanisms, such as their reflection or absorption on surfaces (vertical or horizontal), their diffraction on the edges of obstacles, their refraction by the propagation medium (atmosphere). “These effects are taken into account more or less advanced mathematical models and numerical methods, offering a more or less detailed description of the physical phenomena involved. So-called ‘reference models’ are developed in the time or frequency domain. They may be coupled with each other or even with other models, for example with sound source models and/or atmospheric dynamics models at different scales.” Simulations are used to represent noise sources and to evaluate sound propagation in spatial areas and at given time or frequency intervals. The use of calculation data raises many questions, in particular about the analysis criteria to be used: “Modeling gives access to the level of pressure in the air. This ‘gross’ physical quantity must be interpreted in order to reflect a level of risk or acoustic comfort in the environment. Several treatments are possible: retain a maximum value or an average value in time, in space, associate a number or a duration of exceeding a threshold, etc. The current regulations, for example, translate the sound level in terms of frequencyweighted sound pressure: they thus reflect the human ear’s perception of sound. Research in environmental acoustics allows us to explore other criteria. With fine modeling, it is possible, for example, to evaluate other indicators such as the reverberation time of waves: the speed with which

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they fade can be an analytical criterion that complements that of their level.” Simulations are based on “detailed modeling” or “simplified modeling”: – the former take into account the geometric complexities of the propagation medium and the majority of physical phenomena influencing sound propagation in spaces constrained in terms of spatial extent (street, microdistrict). They therefore require significant computing resources; – the latter, using approximate models, allows global data to be obtained more quickly, on larger spatial and temporal scales. These are used, for example, to map noise (road, rail, air, industrial) over a city. “Reference models” take into account many physical phenomena and represent them in a detailed way. The propagation of sound waves in the air depends on temperature, wind and humidity, so the finest models integrate meteorological data and their evolution in time and space. Since the reflection, diffraction or absorption of sound waves is influenced by many elements of the urban environment, the most accurate models take into account the presence of protective screens, vegetation [GUI 15] or architectural ornamentation, and thus reflect their influence on sound propagation (Figure 7.11).

(a) Assessment of the influence of a right screen on sound propagation around a building [PIC 12]

(b) Assessment of the influence of building greenery on the noise environment of a street at 100 Hz (source: IFSTTAR) Figure 7.11. Acoustic propagation simulations with “detailed modeling”. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 7.11.– The figures provide results of acoustic simulations and represent the pressure field on very short time scales. The latter is obtained using calculations made by means of “detailed modeling”. They account for the main physical phenomena involved in the propagation of sound waves, such as reflection and diffraction by a building with a straight screen (top) and absorption by green facades in a street (bottom). In the first example, the simulation allows to compare different architectural choices (presence of the screen and influence of its shape, presence of absorbent surfaces and influence of their characteristics). In the second example, the calculation represents the sound pressure levels in the street, without (left) and with (right) vegetated facades. It highlights the positive influence of plants on noise reduction in the street for this configuration. Noise levels are represented in color, from red (louder) to blue (quieter). Research on this subject was carried 4

out by IFSTTAR between 2010 and 2014, as part of the “VegDUD” project . This multidisciplinary collaborative project addresses the influence of plants in sustainable urban development through an approach that combines issues related to climatology, hydrology, energy and environmental management. It makes it possible to quantify the influence of alternative practices for collective and private spaces on their acoustic atmosphere, in particular through classical physical indicators such as sound levels and reverberation times (source: IFSTTAR). The three main fields, source characterization, propagation modeling and perception analysis, of environmental acoustics are the subject of continuous research, helping to evaluate and propose effective solutions to the challenges of noise control and reduction. Involving multidisciplinary teams and often carried out in a collaborative context (combining physical and engineering sciences and the humanities and social sciences), this research benefits the entire community and contributes to the development of public policies. 7.3.3. Businesses The location of urban businesses also influences the shape of a city and the lifestyles of its inhabitants, such as the prosperity of merchants. Are there privileged locations in a city for a given business? Is the proximity of one store favorable or unfavorable to another? Is it possible to account for an attraction or repulsion of one trade with another in the same way as Coulomb’s law in electrostatics? (Figure 7.12).

4 Available at: https://irstv.ec-nantes.fr/environnement-sonore-urbain/.

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Figure 7.12. The electrostatic force is attractive or repellent depending on the sign of charges carried by two particles (source: www.commons.wikimedia.org)

COMMENT ON FIGURE 7.12.– Established at the end of the 17th Century by the French physicist Charles-Augustin Coulomb (1736–1806), the law bearing his name forms the basis of electrostatics. Expressing the force of the electrical interaction between two electrically charged particles, it is written as:

where and is the charge carried by two particles, is the electrostatic force exerted by one on the other, is the distance between them, is the permitivity of the void and is an arrow carried by the line connecting the two particles. Coulomb’s law may be stated as follows: “The intensity of the electrostatic force between two electrical charges is proportional to the product of the two charges and is inversely proportional to the square of the distance between the two charges. The force is carried by the line passing through both loads.” Pablo Jensen, a physicist at the École Nationale Supérieure de Lyon, has developed a model that reflects the attractiveness of a location for a given type of business [JEN 06]: “The modeling principle I proposed is based on the analysis of data showing the distribution of businesses in the city of Lyon and identifying locations that are favorable and unfavorable to one type of business or another. The proposed approach uses a calculation formula adapted from physics to social systems. It consists schematically in comparing the actual distance between the shops, classified by given categories, and the distances resulting from a random distribution of these shops throughout the city. This makes it possible to calculate the ‘attraction’ and ‘repulsion’ coefficients of the businesses between them. For example, calculations show that at a distance of 150 meters from a bakery, there are twice as

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many bakeries and twice as many butchers: bakeries repel bakeries but attract butchers...” The analysis of data prioritizing and categorizing the types of businesses for the entire city makes it possible to build a table archiving all the attraction or repulsion coefficients. By quantifying the influence of businesses on each other, they make it possible to map out the location areas that are favorable to the opening of a particular store (Figure 7.13). As with many data processing algorithms, the proposed approach seeks to predict without explaining – no equation, similar to that expressing Coulomb’s law, reflecting the attractiveness of the businesses between them: “The figures that measure these spatial structures do not seek to understand their origin. They transform the reality of the field into quantitative information, in an attempt to answer important questions for traders and planners [...]. This approach is not intended to explain: it proposes an original interpretation of existing location data and draws predictions from it. Its logic is simple: a good location to open a new store is a location that resembles those where other stores of its kind are located...” [JEN 18].

Figure 7.13. The best places to open a bakery in Lyon (source: Pablo Jensen, École Normale Supérieure de Lyon). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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COMMENT ON FIGURE 7.13.– Based on data on the location of shops in the city of Lyon in 2003, a model predicts the best 10% locations to open a bakery. The areas concerned are identified in red on the city map: few of its places already have a bakery – these are identified by black dots. 7.4. A question of choice American biologist Thomas Seeley has spent much of his scientific life studying bees [SEE 10]. For example, he explains how an insect community organizes itself to make decisions that affect its survival: fetch food and find another place to live when the one it occupies is no longer suitable. While each of its members has only fragmentary information on a given situation, a swarm, a community, is able to make a decision that is relevant to everyone’s destiny. According to Yuval Noah Harari, it is even this very advantage that humans have exploited: “What has made us [...] the masters of the planet is not our individual rationality, but our unparalleled ability to think together in large groups (when individuals) know terribly little about the world” [HAR 18].

Figure 7.14. A swarm of bees (source: www.shutterstock)

COMMENT ON FIGURE 7.14.– With more than 1 million described and currently existing species, insects constitute the largest share of animal biodiversity. The study of insect societies (ants, bees, termites) contributes to the development of individual and collective behavioral models [JEN 18]. Some research, such as that reported by biologist Thomas Seeley on bees, testifies to the fact that animals together produce optimal organizational modes from which we can learn and some of which are used, for example, to produce data processing algorithms. It should be noted that the

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scientific community is concerned about the possible disappearance of bees, particularly because of their poisoning by certain pesticides [ARC 18]. Impaired learning, orientation and navigation skills: the consequences of this exposure are multiple. They also threaten the pollination role played by bees, which is essential to many ecosystems. From his observations, Seeley shows how a form of order emerges from chaos and how a group of individuals may make an optimal decision. It also highlights how this decision is reached through interactions between different members of the community and how the energy of a group to defend an option can change the final choice, a form of democratic process. This is part of this researcher’s thesis. Without inviting us to adhere to the myth of an organization as “perfect” as a swarm and to defend the illusion of reproducing its functioning for human communities, the researcher however suggests, based on his observations, that an optimal decision is generally based on: – a diversity of knowledge about possible options; – a sincere and honest sharing of information on possible options; – independence in the evaluation of options by everyone; – a confrontation of everyone’s opinions on these different options; – leadership that encourages discussion, without the intention of dominating it. These principles are in part what some citizens expect from a genuine democratic process and Seeley claims to apply them to decisions concerning the life of his laboratory (recruitment of a researcher, promotion of another, response to a call for projects, etc.). Rich in some lessons from the mechanics of hives, let us now move on to the mechanics of the Web, while keeping in mind the question of the choices of societies. With social networks and the mass of data they convey [AME 17], it is possible to observe, in the manner of an entomologist, how certain political communities are structured. Noé Gaumont, a young computer researcher studying the structure of dynamic networks [GAU 16], explains: “An increasing amount of data is available to researchers to study and model animal or human societies. I am interested in graph analysis algorithms, which make it possible to detect ‘communities’ (political, religious, scientific, sports, etc.) within sets of relationships. A community is characterized by a set of nodes that are strongly connected to each other and weakly connected to the network within which it operates.”

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The study of graphs is a specific branch of mathematics, initiated in the 18th Century when Leonard Euler proposed a mathematical solution of the problem of the “seven Königsberg bridges”. From a given point in the city, it is a question of finding a walk that brings you back to that point by passing once and only once through each of the seven bridges in the city of Königsberg. The problem turns out to be that there is no solution. In order to show this result, Euler reasoned in the absurd, using a graph to represent the desired walk and reach an impossibility. A graph G = (V, E) consists of a set of points (V) and a set of links (E) between these points. It can be represented by a matrix M whose component m is 1 when the nodes v and v are linked and 0 if not. Matrix algebra thus provides a formal framework for the study of graphs, which model complex systems: “The matrix description makes it possible to represent a graph statically, but not to account for their dynamics. My research has thus contributed to the development of a new matrix representation of graphs, integrating their evolution over time – discretely (at given times) or continuously (over a time interval).” This work, which is essentially theoretical, has found practical applications, particularly in the context of the 20175 French presidential election campaign. They have helped to highlight how certain communities are structured on the Internet, around political themes and issues. “We analyzed the data from the Twitter network to understand the dynamics of the 2017 French presidential campaign and to visualize how political communities are structured over time. We followed the publications of some 3,500 politicians (elected officials, party members, etc.) and the reactions they generated among other users of the network (retweet, quotation, response, etc.). Out of 2,500,000 accounts interacting with these personalities, we have selected 200,000 accounts to establish a fairly clear political affiliation with a particular candidate for election. This small panel is then used for our analyses of the dynamics of political communities on a social network.” A social network on the Internet lends itself quite naturally to a mathematical description according to graph theory. Each account being a node, the challenge of

5 For this type of study, researchers respect legal obligations and obviously take precautions – hence, the data collected are anonymized and stored in a secure manner. “Such research, carried out between February and April 2017, i.e. before the entry into force of the DGMP and a change in the terms of use of the Twitter network, would no longer be possible as it stands today”, stresses Noé Gaumont.

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the mathematical representation of the network is to find a relationship between the nodes: “The criteria leading to the identification of a relationship between nodes are numerous. In our model, we chose to connect two nodes when the first node relayed at least three tweets from the second node over a two-week period. We describe a graph dynamically and then use a ‘community detection’ algorithm. This is obtained by partitioning the nodes in the graph according to the following principle: ‘each node in the community belongs to a single community and is more strongly connected to this community than to the rest of the network’. Assuming that this identified community is a ‘political’ community, we are looking for some of its own characteristics.” Among these, the semantics used during the campaign. What are the themes that interest this community most? How are ideas conveyed? Which keywords are most commonly used? The data provide interesting insights for researchers to understand the expectations of each community. They can also be used to draw a group portrait: “Are the identified communities ‘open’ or ‘closed’? It is for example by understanding how they seek and disseminate information that we can propose to characterize a political community. Data analysis highlights the dynamics of the campaign, the anchoring of a discourse within a community, the loyalty of members to a political program, etc.” Inventing, relaying, propagating and exploiting false information, rumors, but also fighting them, refuting them, contradicting them, is perhaps a phenomenon inherent in any political campaign. If it acquires a new dimension with social networks, served by an ever-increasing speed of propagation or scope of diffusion, this phenomenon is not new. The summer of 1789 in the Kingdom of France gives, with “La Grande Peur” (“The Great Fear”), an example of the rapid propagation of unverified information (Figure 7.15). Using their analysis tool, the researchers were therefore also interested in the different uses of the digital information sources that the communities observed with their algorithm use (Figure 7.16). “This is an example of an application of our algorithm, with which we followed the distribution of ‘fake news’ during the 2017 French campaign. For the exercise, we used as a basis for our work a list of false information compiled by journalists from the French daily Le Monde in a section dedicated to their refutation. While this reference is not exhaustive, it has allowed us to highlight the divisions and polarizations that misinformation generates among the political communities participating in the campaign.”

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The algorithm developed by the researchers is not universal and it is used with knowledge of its limitations: “The definition of the ‘political community’ we have proposed is questionable: in particular, we assume that it is characterized by the candidate around whom the users of the Twitter network are structured. Our methodology does not allow us to identify all communities and remains limited to a single social network, Twitter representing only a part of the community of citizens. The model we use is also sensitive to the criteria for evaluating relationships between Internet users: for example, relaying a tweet does not necessarily mean adhering to the information concerned...”

Figure 7.15. A historical example of the rapid spread of unverified information during the summer of 1789 in France

COMMENT ON FIGURE 7.15.– The strange episode of the French Revolution, known as the “Great Fear”, illustrates certain mechanisms for the dissemination of news and the formation of popular movements [LEF 73]. It questions the mysterious alchemy that history sometimes gives birth to. In the summer of 1789, an unexpected revolt of the countryside took place in many provinces of the Kingdom of France. Despite the collection of grievance books and the meeting of the States-General, none of the concerns of the vast majority of small farmers had been raised. The

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feudal and a seignioriaal regime, perrpetuating thee privileges of o the nobilityy and the clergy, thhe piling up of o multiple taxx floors, the status s of the laand – and quiite simply the miseery of a large number, reinf nforced by a subsistence s crrisis had beenn growing for morre than a yeear and caussing numerou us agrarian disorders. W What was happeninng in Versaillles and Pariss encouraged action. In thhe second half lf of July, rumors spread thatt hordes of bandits, wh ho were thoought to be perhaps t aristocratts, were causing damage to t villages annd crops. instrumeentalized by the People armed themsselves with forks fo and sho otguns, and the tocsin sometimes soundedd the alarm. When W the empptiness of thiss fear broke out, it turnedd into an b becausse people insurrection. Some caastles were atttacked by peassants – some burned e th he many seigneeurial rights. How was were tryiing to find thee documents establishing all this possible p in a large l part of the t Kingdom of o France andd in such a shhort time? How weere the newss, false and true, circulatting there? By B mail com ming from Versaillees or Paris inn a few days.. Thanks to th he visits at loong distancess between families and friends. By the distaant echoes off the tocsins, the smoke off burning v from afar a in the coountryside, an nd the newcom mers from neiighboring castles, visible towns. Peddlers, P who traveled the Kingdom’s K roa ads by the thoousands, had llong been the “soccial networks of the time”. They disseminated or invented informaation that went witth the times. The times weere hostile to the nobles, who w were alsso feared, while theey were less respected. r One of the remarkable conseqquences of thiis episode was the night n of August 4, 1789 – abolishing a certain privilegess, but not resoolving the issue of peasant p property. From thhis example, we w can conceive that the peeddlers of yesterday ay and the soccial networks of o today appeear more as veectors of certaain social and polittical movemennts, but are noot their root ca auses.

Figure 7.16. 7 Analysis of information n relayed on Twitter T during the t French pre esidential n 2017 [GAU 18]. 1 For a color version of th his figure, see campaign in www.iste.co o.uk/sigrist/sim mulation2.zip

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COMMENT ON FIGURE 7.16.– The figure represents an analysis of the information relayed on Twitter by different accounts, identified in community by an algorithm, during the 2017 French presidential campaign. Each community is associated with a color (red, pink, violet, blue, purple, brown). A list of false information is taken as a reference. Their diffusions (yellow dots) and rebuttals (green dots) are monitored over the period from February to April 2017. Intended for social and political science, the tool, coupled with other algorithms, also makes it possible to understand and evaluate the influence of automated and simulated accounts. As the Agora of the 21st Century is being digitized, algorithms make it possible to understand its driving forces and they also find applications in other fields: “Algorithms identifying groups of networked users are nowadays receiving the attention of many private companies in order to develop online commerce. It is also part of the arsenal of tools contributing to improving the reputation and digital reputation of brands, companies, etc.” NOTE.– Information generated by algorithm. Since its invention at the end of the last century, the French literary movement OuLiPo has proposed, among other things, to apply certain mathematical concepts to the construction of written texts, thus demonstrating the links between literature and mathematics [OUL 73]. The French writer Raymond Queneau (1903–1976) used combinatorics, for example. From 10 proposals for the 14 verses of a sonnet, he created Cent mille milliards de poèmes. 10 possible choices for the first verse, 10 possible choices for the second give: 10×10 or 102 or 100 possible poems. With 14 verses: 1014 poems or 100 Tpoems: the 100,000 billion of the title of the book [QUE 61]. Randomly chosen from a book that does not take up much space in a library, we read a realization of a literary random variable, which can begin as follows: “Du jeune avantageux, la nymphe était éprise (from the young advantageous, the nymph was in love) // pour déplaire au profane aussi bien qu’aux idiots (to please the laypeople as well as the idiots) // La découverte alors, voilà qui traumatise: (the discovery then, here is what traumatizes:) // on espère toujours être de vrais normaux! (we always hope to be true normals!).” In another book, Queneau tells the same story 99 times, with variations in style [QUE 47]. Nowadays, automatic learning techniques are used in an experience similar to the oulipian approach and a style exercise dear to Queneau. They use

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language models, whose applications are nowadays very varied: speech recognition (acoustic techniques) or writing (optical techniques), correction or automatic translations. Two main families of modeling exist: modeling based on the use of formal grammars is developed by experts in linguistics, when stochastic modeling attempts to automatically describe a language based on the observation of a set of texts. Mathematically, a stochastic language model assigns a probability to a sequence of is assigned words – for example, a sentence of M words, noted W = (w ) a probability of P(W ). Estimating the relative probabilities of different sentences is useful for many natural language processing applications, such as those that produce texts. Based on these probability distributions, language models are able to predict the word (or sentence) that can follow a given word or sentence, just like the automatic writing assistants on our mobile phones. A language model can be based on learning techniques: it learns the probability of a word or sentence occurring from a set of texts. The simplest models, the current majority, will seek to learn from the context in which a word or sentence appears, while the more elaborate, less common models, will learn from whole paragraphs. Models based on neural networks are constantly developing and offer performances considered interesting for performing the learning tasks required by a language model: “Neural network models solve some of the shortcomings of traditional language models: they allow conditioning on increasingly large context sizes with only a linear increase in the number of parameters, they alleviate the need for manually designing backoff orders, and they support generalization across different contexts” [GOL 17]. For example, a language model is developed by researchers from the Open IA research consortium. By learning on nearly 10 million web pages, the model, built on more than a billion parameters, is able to produce a coherent text from a sentence, respecting its context and style (Figure 7.17): “[The program] generates synthetic text samples in response to the model being primed with an arbitrary input. The model is chameleon-like – it adapts to the style and content of the conditioning text. This allows the user to generate realistic and coherent continuations about a topic of their choosing…” [RAD 19] The authors of the program emphasize that, like many artificial intelligence tools, it remains to this day dependent on the data on which it learns.

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Figure 7.1 17. Example of o automaticallly generated text t [RAD 19]

COMMENT ON FIGUR RE 7.17.– A fiirst sentence gives g the subjject and style of a text: the theft of a train carrying sensitive equ uipment is reported accoording to journalistic codes. An A artificial intelligence program p prodduces a coheerent text, imitatinng the journalistic processiing of informa ation. Thus, it i is able to geenerate a coheerent and fluid d text every other o time wheen it uses well-doocumented exxamples and it i fails for verry specific toppics for whichh the data remainn fragmented.. The automaatic text prod duction tool also suffers from the limitatiions inherent in this type of program, such as the excessive e repetition of certainn terms or abrrupt transitionns from one su ubject to anotther, a limitatiion that a journallist or writer’ss style does noot show.

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Having language models also makes it possible to develop automatic reading comprehension programs, some of which perform as well as humans on reading tests [HAR 19]. Despite its current limitations, the designers of this program explain that this type of tool, made ever more efficient, opens the way to many uses: conversational agents, writing assistants, speech recognition systems, etc. Some uses can obviously be fraudulent [HER 19]: spreading false news on the Internet, false articles on social networks and reinforcing certain online scams, such as phishing [AMP 14]. Such an experience, both literary and digital, can invite us to rethink our relationship to information, as its authors point out: “These findings, combined with earlier results on synthetic imagery, audio, and video, imply that technologies are reducing the cost of generating fake content and waging disinformation campaigns. The public at large will need to become more skeptical of text (and images) they find online…” [RAD 19] 7.5. What about humans? At the zenith of an afternoon of full sunlight, a man stands at the crossroads of two highways, bordered by fallow fields and expanses of wheat. Strange place for an appointment: long minutes of waiting, deafening silence and heavy light. A car or a truck pass by without stopping and then this small plane flying at low altitude appears on the horizon. Running for his life, the man had to flee from this biplane that was angry with him for a reason that was still unknown [HIT 59]. Stress and the race for life are embodied by the American actor Cary Grant (1904–1986), in this masterful scene of the masterpiece of British director Alfred Hitchcock (1899– 1980), North by Northwest. No dramatic music for an action taking place in full light: the usual cinematographic codes are shaken up and the spectator’s anxiety rises to the highest level! Cary Grant simulates the marks of fear on his face: the character he plays is supposed to go from anxiety to terror in this scene, experiencing all the modulations of this emotion, which the website www.atlasofemotions.org lists (Figure 7.18). The site was created by the American psychologist Paul Ekman, who, since the late 1970s, has been studying human emotions. His research has led him to publish numerous books on the subject [EKM 03], as part of a humanistic approach. Empathy, the understanding of emotions and the ability to adapt to them, is, according to him, one of the keys to greater harmony among human beings.

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Emotionns are also forr them a matteer of individual survival [C CUR 14] and ccollective life [RIC C 13], also underpinning u our decision--making and action: “Emootions are essentiall for humans to guide reasoning and alllow adaptationn – they definne a goal and mainntain a state too achieve it...”” [TIS 18]

Fig gure 7.18. The e different form ms of fear (sou urce: www.atla asofemotions.org)

Paul Ekman wishees to list all human h emotio ons, and classsify them according to their inttensity, their duration. Hee makes thesee data availaable in order to name emotionss, in all their subtleties s and nuances. In 2015, 2 an animation film prooduced by Pixar Stuudios was insspired by his research and d staged thesee emotions [D DOC 15]. Accordinng to Ekmann, recognizingg them in on neself and in others helps to bring human beings b closer together. t Fear,, joy, anger, saadness, surpriise and disgusst would be sixx emotions coommon to all humaan beings thaat would affeect human faaces in differeent ways. In order to identify similarities (or ( differences), he helped d develop a digital d tool, thhe Facial Action Coding C Systeem [EKM 788, EKM 80, EKM 93], used today bby many psycholoogical researchhers (Figure 7.19). 7

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Figure 7.19. Examples of Action Units (AU) from the Facial Action Coding System for human expressions

COMMENT ON FIGURE 7.19.– According to Ekman, facial expressions, elements of human communication, imprint on an individual’s face his internal emotional state, and, in some situations, can betray his hidden intentions. Emotions are communicated by almost imperceptible changes in one or a few facial features: anger is manifested, for example, by a narrowing of the lips, sadness by a downward movement of the corner of the lips. The so-called FACS software has been developed to automatically detect the subtlety and variety of human emotions, and certain nonverbal communication traits. It is based on the empirical observation of human faces through analyzed slow-moving video recordings. In this way, researchers establish a classification of facial expressions, coded in the FACS as Action Units (AU), that can occur individually or simultaneously [DU 14]. The figure above gives some examples, based on the observation of muscle movement around the eyes and lips. It should be noted that, doing so, psychological researchers refer to facial expression modeling. Facial expressions were studied before Ekman by the painter Charles Le Brun (1619-1690) in the 17th Century. His drawings of the features on human faces were

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publisheed posthumouusly in 1727 (Figure 7.19)). In the 19thh Century, thhe French physiciann Guillaume-B Benjamin Ducchenne (1807–1875) helpedd to establish a map of facial exxpressions. Hee used a devicee that produceed electrical im mpulses and sttimulated facial muuscles (Figuree 7.20).

(a) La Colère, C Charle es Le Brun, 1727, from Exp pression des passions p de l’’âme (source: www.gallica.b bnf.fr)

(b) Guillaume-Ben G njamin Duche enne triiggers facial exxpressions on na patien nt’s face during g his research h using electrical e stimu ulation (source e: ww ww.biusante.parisdescartes.fr)

Figure 7.20. Observing and reprodu ucing facial exxpressions

Duchhenne publishhed in 1862 thhe Mécanisme de la physiionomie humaaine – ou l’analysee électro-physsiologique dee l’expression des passionss. From his reesearches for instaance, Duchennne has shown that a real sm mile is not onlly characterized by the contractiion of the muuscles of the mouth, m but alsso by the conttraction of thee muscles surroundding the eye.. This contraaction would be almost im mpossible to perform voluntarily and not sppontaneously, so that a sinccere smile woould be distinct from a mpossible to siimulate. sneer and would be im Duchhenne in the 19th Century and a Ekman in the 20th Centtury initiated w work that extendedd into the 21st Century with digital techniques. At A the conflluence of psycholoogy, computer science, neuuroscience, au utomation, beehavioral andd learning sciences, some researrchers are devveloping systeems with the capacity to recognize, man emotions [PIC 97, JEO O 17]. This new branch express, synthesize annd model hum of compputing is callled affective computing, the computiing of emotiions. For

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example, it aims to design machines capable of decoding human emotions6 and adapting to them. Research in affective computing has potential applications in many areas [CAM 16], such as marketing and advertising. Created in 2009, the American company Affectivia (www.affectiva.com) develops and markets, for example, Affdex emotion recognition software, analyzing facial expressions and tone of voice. The company claims to have the most extensive database to date on the emotional responses of Internet users or viewers watching digital content (advertisements, music videos, ads, etc.). These data allow the software to predict the effectiveness of an advertising message according to different criteria (geographical, social, cultural, ethnic or generational) in order to propose targeted campaigns [CAM 16]. In the United States, the Emotion Computing Group at the University of California (www.emotions.ict.usc.edu) and the Emotion Research Group at MIT (www.affect.media.mit.edu) are among the pioneers of this field of research, which is developing in many countries (including France, China, India and Iran) that organize conferences dedicated to this subject. The company mentioned above is a start-up created by MIT and its research teams in this field. In France, several laboratories are interested in affective computing, including LIMSI, where French researcher Laurence Devillers works. She thus defines the objective of its work: “To make interaction with the machine more natural, we try to build the profile of the person we are talking to by detecting emotions – anger, fear, joy, sadness – which allows the machine to adapt its response...” (remarks reported by [LEG 18]). This research is undertaken above all to improve the complementarity between human and digital intelligence [GAR 06, KAL 17], for example in order to develop a “social robot”. Simulating the characteristics of living organisms, the latter is designed to replace the human. To do this, it has a set of computer equipment and programs that allow it to perceive their environment and interpret perceived signals – in particular the recognition of human speech and emotions. The robot is designed to make decisions based on perceived, recognized, and also stored information from the environment, based on dedicated algorithms. Using mechanical devices it performs different actions in the physical world, such as producing oral responses through speech synthesis. It can thus potentially perform surveillance, assistance and

6 It should be noted that emotions can also be detected indirectly, for example with the analysis of physiological data [GOU 11, NAE 16, RAG 17, WIO 17] or vocal expressions [BAZ 15, JOH 06, COW 18] – or even the composition of tears, as shown by the work of the American photographer Rose-Lynn Fischer [FIS 17].

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social interaction tasks, particularly with people suffering from psychological (such as depression) or neurological (such as Alzheimer’s) diseases [RIV 13, CHI 17]: “A robot expressing empathy can be used to explain, educate, reassure the people with whom the machine interacts. [It can contribute to] the cognitive stimulation of elderly people with diseases such as Alzheimer’s disease. A robot can react with pseudo-affective behaviors. The patient then plays with the robot as if it were a pet, which stimulates him emotionally and creates a social bond” (remarks reported by [LAU 18]). The social robot remains, for the researcher, a machine. It is far from replacing humans in what is specific to them: “Robots feel nothing, have no emotions or intention. This is a simulation. Even if (we) manage to produce a ‘benevolent’ robot, (it) is only modeling...” (statement reported in [LEG 08]). The development of social robots has led some researchers to rethink the relationship between humans and machines: “Seeing emotions manifested by humans or robots activates the same areas of the brain in a relatively similar way. We will have to live with machines with which we interact as with humans, knowing that they are not humans” [TIS 18]. Despite advances in mechanics, automation and computer science, robots are still distant cousins of humans, whose memory, body and face remain to this day of unique beauty and complexity. While traveling through the California desert of the Death Valley in the late 1970s, French photographer Jeanloup Sieff (1933–2000) filmed the features of Vaugnet Rollins, a cook he met in a snack bar [SIE 11]. Expression lines and the intensity of his gaze are rendered by a print that highlights them (Figure 7.21). The photograph materializes a portrait that would have aged at the same time as its model, unlike Dorian Gray’s face, frozen in a smooth, cynical and eternal youth [WIL 90], like that of the robots that will one day become our companions. It offers to imagine the life of this woman, contemplating the grooves dug on her face by the time and emotions that have been imprinted on it. Some scientists use these traits to create robots that look like them. In 2017, Japanese robotician Hiroshi Ishiguro introduced Erica, a humanoid robot of his creation, according to him, the most successful to date. The British newspaper The Guardian has even dedicated a mini-documentary video to her7. Erica is 23 years old. She interacts with humans by answering their questions, she expresses herself in a crystal-clear voice and sometimes lets slip a little mechanical laughter suggesting 7 Available at: https://www.theguardian.com/technology/ng-interactive/2017/apr/07/meeterica-the-worlds-most-autonomous-android-video/.

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that she captures human humor. A sophisticated learning program allows her to adapt to the conversation. If her silicone face is not marked by emotions, she has a small smile on her face. Equipped with infrared sensors, she detects the presence of humans beside her and recognizes their facial expressions. She is capable of movements enabled by a system articulated at 20 degrees of freedom (the first simulation models used by mechanical engineers included as many before reaching several hundred thousand nowadays). Erica may present a TV news program [GAR 18]... Its creator wonders: “What does it mean for us to be ‘human beings?’”

Figure 7.21. Vaugnet Rollins, Jeanloup Sieff, 1977 (source: © Jeanloup Sieff)

In the early 1950s, when modern concepts of artificial intelligence were born, the American writer Ray Bradbury (1920–2012) imagined a futuristic world where omnipresent screens overwhelmed the imagination and the critical sense [BRA 53]. Permitted by books, imagination and reflection become suspicious, as do the paper materials they use. Firefighter Montag was assigned to a special unit, collecting and destroying books, whose pages burned before his eyes at a temperature of 451°F. This act, like the society in which he operates, goes against his deep identity. His quest for freedom led him to find the Hommes-Livres, preserving human knowledge, memory, sensitivity and creativity by memorizing the lines of the greatest works of literature and adopting their title as his middle name. Making mistakes – of judgment, analysis or interpretation – and basing some of our choices on criteria that cannot be reduced to an equation or data, in other words, claiming our subjectivity, freedom and imperfection, might be a first step in answering the question posed above.

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The mechanical prowess of robots or the numerical prowess of algorithms will not immediately and irreparably divert us from those of humans. The beauty of a rugby or football match lies in the richness, diversity and fluidity of coordinated human actions as well as in the uncertainty of their achievement. Some movements, considered perfect, such as the kick of an extraordinary sportsman like Jonny Wilkinson, are acquired at the cost of efforts and sacrifices made by humans who are often extraordinary, at the limits of their bodies and psyche [WIL 01]. Some photographs of the French photographer Henri Cartier-Bresson (1908– 2004) are models of mastery of space and time, at the service of the emotion and beauty of a suspended moment. Gifted with an extraordinary sense of composition, he says he was influenced in his formative years by the work of Romanian mathematician and diplomat Matila Ghyka, The Golden Number. Cartier-Bresson pays particular attention to the lines that structure an image in some of his photographic compositions. And sometimes in a mathematical way, he researches on certain cliché elements of geometry in order to make his art a science of the living. He also explains the notion of the decisive moment, which can be understood as a presence in time and space, as well as mechanics: “Composition must be one of our constant concerns, but when it comes to photography, it can only be intuitive, because we are dealing with fleeting moments when relationships are shifting...” [CAR 96]. The golden number seems unconsciously engraved in the viewfinder of his Leica camera, with which he captured the fleeting moments. One of his photographs, Ile de Sifnos, published in the collection Les Européens [CAR 97, p. 115] is a model of composition based on forms and a furtive moment when a silhouette breaks in. Looking at it, I find it reasonable to believe that imagination, intuition, sensation and emotion – some would say consciousness [KOC 12] – will remain the hallmark of human beings and their freedom, whether or not assisted by technology.

Conclusion A Digital World

Digital modeling changes technical practices and develops scientific knowledge: the many testimonies of researchers and engineers gathered in this volume provide an eloquent illustration of this. While the physical sciences, and mechanics in particular, were among the first to resort to numerical modeling and simulation, we have outlined how this trend has developed in many other disciplines. In summary, let us retain from our presentation the following lines of emphasis, complementing those presented at the end of the first volume. A global technique: In order to be developed as a technique in its own right by a country, numerical simulation requires high-level skills. These are held by mathematicians, physicists, computer scientists, engineers and researchers. A broad scientific community contributing to: – developing physical or mathematical models of a phenomenon or set of phenomena of interest for a given discipline or application; – developing and validating computational algorithms to produce the data, used for design, production or marketing purposes; – operating the computer resources that carry out the simulation algorithms (software and computing machines, with their associated infrastructures, from personal computers to supercomputers); – imagining the most varied applications because of their scientific or economic interest. Countries that now master the entire technique, including the United States, China, Japan, and some European countries (among which France and Germany), are still in small numbers.

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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A generalized technique: Numerical modeling helps to renew the practice of many scientific disciplines, particularly those that use complex models – such as those of the Universe, climate, the human body and energy – that involve multiphysical, multispecies or multiscale phenomena. Numerical models are a collection of knowledge shared by a scientific community. They testify to the stateof-the-art at a given moment and are continuously enriched by new elements. The results of simulations are interpreted, among other things, with regard to the assumptions on which the models are built and/or the reliability of the data they use. There is always a human dimension to the interpretation of results whose criticism is based on the limitations of using digital tools, assumptions associated with models or practices commonly constructed by a scientific community. While numerical simulation helps to establish recommendations and make decisions (technical, economic, political or other), it is only one tool among others (such as data, measurements, or experimental observations) that it does not replace. Modeling remains imperfect: to date, it has not been possible to fully and accurately account for complex phenomena and, in the case of real systems, models are most often used in a comparative rather than predictive way. Collective innovations: Numerical simulation is related to communication and information technologies, whose development, dating back one or two decades, has its roots in the second half of the last century. Some major companies in this field are nowadays commercial and global successes, attributed to outstanding personalities. A media story accompanies their success and sometimes suggests the myth of the brilliant and solitary innovator. This may mean forgetting that scientific discoveries are both individual and collective. Technical inventions are made in different parts of the world in different ways – sometimes simultaneously, in a given context: economic or cultural competition, diplomatic or military supremacy. Major industrial projects all require significant public investment. Risk taking is above all collective and sometimes the most ambitious technical projects, based on engineers’ dreams, simply do not see the light of day [CHE 09]. Even if we obviously need an idea, a strength of character, a confidence in your intellectual capacities, as well as a chance to propose and believe in a large-scale project, we never think and innovate alone [ENG 03, HAR 18], that is to say independently: – a political, social or economic context; – pre-existing knowledge produced by others; – currents of thought (and fashions: they also exist in science!); – collectively funded infrastructure (transportation, communication, training, etc.).

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Innovation genius takes shape, in a spectacular way, in an ability to think outside the box to approach problems in a different way by introducing a disruption* into a scientific, technological and economic environment, and to integrate the elements of an existing one. Depending on their personality – in a combination of deep motivations, connection to the world, personal history and the influence of an environment – some transform an idea into a flourishing company or industrial group, such as American entrepreneur Steve Jobs (1955–2011) [BOY 15]. Others selflessly offer the fruit of their reflection to the scientific community, such as French mathematician Alexander Grothendieck (1928–2014) [SCH 16]. Many researchers and entrepreneurs with a spirit of innovation are familiar with the sources of discovery. Ambitions, doubts, successes, disappointments, competition, rivalry, emulation and cooperation are their daily lives. The vast majority of them also experience innovation as incremental, far from the characteristics attributed to disruptive innovation! These words are attributed to the French engineer Henri Dupuy de Lôme (1816–1885), a 19th-Century innovator: “When you have such considerable innovations in mind, you have to wait for the right opportunity to make them succeed; otherwise you break, without profit for anyone, against the astonishment of the people that nothing has prepared to listen to you” [https://fr.wikipedia.org/wiki/Henri_ Dupuy_de_Lôme]. They remind us that innovation requires taking risks and supposes benefiting from a combination of favorable events, which are not always present. Failure, always relative, is as much a part of the daily life of researchers and innovators as success. It is one of the realities of research and development that we often prefer to ignore in order to focus on success, considered more attractive and remunerative. These failures do not prevent women and men from inventing, undertaking and innovating, every day, in a way that is more or less visible to others. On the contrary, failure may even be a condition of scientific research [FIR 15]. Collaborative research and versatile researchers: The collaborative mode is becoming a necessity for some research actors, both public and private, as Yazid Madi, researcher at the École Polytechnique Féminine, testifies: “A researcher sometimes has to develop engineering skills: understanding industrial realities and methodologies helps to guide research in a relevant way – and raises exciting academic questions! In engineering sciences, it is quite possible to carry out high-level scientific research with an industrial partnership.”

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As we have mentioned several times in the two volumes of this book, numerical simulation and modeling techniques are partly the result of collaborative developments, often carried out in an international context. Knowledge is essentially porous and it is therefore difficult to draw clear dividing lines between various intellectual areas. Referring to numerical simulation, we also encountered other techniques, such as artificial intelligence, and we questioned some of the uses made possible by applications from the digital world and the techniques they allow to develop. Numerical simulation also contributes to major scientific or technical engineering projects, meeting the fundamental human need to understand, explore and adapt to the world. Many of them – such as observation of the Earth, the Universe, understanding climate and ocean dynamics, improving or researching energy production processes, analyzing living data and biodiversity – involve interstate scientific cooperation, sometimes going beyond the specific interests of each nation. These give a positive meaning to the progress of knowledge in a context where the challenges of the 21st Century seem unprecedented in the history of humanity. A clear statement of the dangers and threats that characterize them can also be accompanied by a form of optimism about the assets that humanity still has to face them [HAR 18, PIN 18a, PIN 18b]. Some techniques will undoubtedly contribute to meeting these challenges and we have outlined how numerical simulation proposes advances that already contribute to them, contributing to the reliability of technical solutions, a more sober or sustainable use of objects, a better use of our resources or collective decision-making. These technical solutions will, among other things, enable humans to adapt to living conditions that will be profoundly altered by current climate and ecological changes, some attributable tour actions on our environement. Humanity is nothing without technology and technology alone is nothing [CAR 14, ORT 17]. Most of the human contributions, such as creation, imagination, contemplation, intuition, reflection and introspection, to the world are beyond technology’s grasp [CAN 17, MIS 11, SCH 12]. Everyone can state which of these contributions matter to them and give back the salt of life, while digital technology changes our relationship to the world. Creations and destruction are in some respects two sides of the same coin, which is often difficult to accept together. Favoring the former by limiting the latter requires humans to make conscious collective and individual choices – some of which can use techniques. To this day, they remain the freedom of women and men – starting with the freedom to question their use and purposes and to act accordingly on a daily basis, according to one’s means and values. The mastery of digital techniques and their dissemination involves both their designers and users, current and future. It is one of the challenges of the 21st Century – the example of artificial intelligence being one of the most emblematic today. Many scientists and engineers working in different sectors do not act

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indiscriminately without constantly questioning the purpose of their research. They also contribute to the development of techniques with a humanistic goal, still oriented toward the idea of progress – the improvement or maintenance of good living conditions for most of humanity. They act without naivety, developing an awareness of the limits of their actions vis-à-vis economic or other powers, which can exploit these techniques for other purposes. When they have the independence, freedom and protection that this implies, the most enlightened of them bring the fruits of their research and reflection to as many people as possible. A status, as public research in France today offers them, allows them to do so. Some nowadays see such statutes as a privilege reserved for a minority and granted at the expense of the majority – or as a brake on industrial innovation. It means forgetting that it is at the same time an opportunity for the whole community: the opportunity to remain in control of one’s own destiny. Beyond unforeseen situations whose probability and safety researchers and engineers try to assess, the risks associated with the development of a technique more certainly lie in their unequal diffusion and especially in their unlimited use for destruction, domination or manipulation. At the collective level, this would be done by humans, especially those of us who have and will have the economic, political or ethical power to guide decisions, not machines or algorithms, even if these resources would be useful for this purpose. The use of a technology is a matter of choice under constraints beyond the majority of humans in their daily lives – in particular, the economic or political power relations and the subtle injunctions of the social system in which they live. In order not to despair collectively of the technologies that humanity also needs in the 21st Century, I believe that the definition of a common decency, the primacy of political choices, involving living together and human values, over economics and technology, remains one of the decisive safeguards. If it is also one of the most difficult to support, humanity still has this possibility to this day. We are obviously largely incomplete in stating this. The purpose here is to talk about a brick that fits into a larger technical building. It is up to each of us to complement it with other resources and perspectives – historical, political, economic or philosophical. Between Prometheus and Cassander, these words, well-known to the French humanist and writer François Rabelais (Figure C.1) – which some believe the 21st Century will make obsolete – invite us more than ever to continue to question the meaning of the techniques and, beyond that, the conditions in which they are constructed. To do this, it may be a matter of trying to understand how they are created, how they can be controlled and used by humans, for the future of humans – with machines.

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Figu ure C.1. Franççois Rabelais (1494–1553), ( anonymous, 16th 1 Century, oil on canvas, Château de Versailles V

COMMEN NT ON FIGURE E C.1.– A 16th h Century French writer, Raabelais was thhe author of the faamous aphoriism “science without consccience is but the ruin of thhe soul”. These woords can be foound in the lettter he had Ga argantua writee to Pantagruuel, two of the mainn characters in i his novels. The father’s words trace for f his son a humanist path of life, l based, am mong other thhings, on knowledge: “I coommit you to use your youth to progress welll in knowledgge and virtue [...] [ That theree be no scienttific study mory and for this t you will help h yourselff from the that you do not keep in your mem universaal encyclopediia of the authhors who deallt with it [...] When you reaalize that you havee acquired alll human know wledge, return n to me, so thhat I may seee you and give you my blessing before b dying” ” [RAB 32].

Glossary of Terms

Organizations cited CEA The Commissariat à l’Énergie Atomique et aux Energies Alternatives (Commission for Atomic Energy and Alternative Energies) is a French public research organization of a scientific, technical and industrial nature. In France, the CEA’s 16,000 employees, nearly a third of whom are women, work in its nine French centers. They are involved in four areas of research, development and innovation: defense and security, nuclear and renewable energies, technological research for industry and fundamental research (material and life sciences). Relying on a recognized expertise capacity, the CEA participates in the implementation of collaborative projects with numerous academic and industrial partners. It is intended to contribute to technological development and the transfer of knowledge, skills and techniques to industry. The CEA was decided by French President Charles de Gaulle (1890–1970) in 1945, in the aftermath of the Second World War, when the various uses of nuclear energy took on a modern strategic character. France’s political ambition is to carry out “scientific and technical research with a view to the use of atomic energy in the various fields of science, industry and national defense”. Nowadays, CEA’s missions have been adapted to many new scientific challenges – in particular those of life sciences and the environment. www.cea.fr

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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CEREMA The Centre d’Etudes et d’Expertise sur les Risques, l’Environnement, la Mobilité et l’Aménagement is is a French public institution whose work meets the major societal challenges of sustainable development and the management of territories and cities. CEREMA is a technical expert in various fields (development, transport, infrastructure, risks, construction, environment, etc.) and contributes its knowledge and know-how to improve the living conditions of citizens. Focused on supporting the French State’s public policies, CEREMA is placed under the dual supervision of the Ministry for the Ecological and Solidary Transition and the Ministry of Territorial Cohesion. www.cerema.fr CERFACS The Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique is a fundamental and applied research center in France. Created in 1987, it specializes in numerical modeling and simulation. Through its resources and know-how in high-performance computing, CERFACS addresses major scientific and technical problems in public and industrial research. Its mission is to: – develop scientific and technical research aimed at improving advanced computing methods, including better consideration of the physical processes involved, and the development of high-performance algorithms for new ECU architectures; – provide access, either on its own or in shared mode, to new architecture computers that can provide significant performance gains; – transfer this scientific knowledge, for application, to major industrial sectors; – train highly qualified personnel and provide advanced training for the selected sectors and areas of application. CERFACS teams include physicists, applied mathematicians, numerical analysts and computer scientists. They design and develop innovative methods and software solutions that meet the needs of the aeronautics, space, climate, energy and environment sectors [HUE 98]. www.cerfacs.fr

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CETIM The Centre Technique des Industries Mécaniques is one of the leading industrial technical centers in France. Created in 1965 at the request of French mechanical engineering manufacturers, CETIM’s mission is to provide companies with the means and skills to increase their competitiveness, to participate in standardization, to make the link between scientific research and industry, to promote technological progress and to help improve efficiency and quality assurance. CETIM has three main missions: the execution of and participation in shared research and development activities, the implementation of a global and personalized offer of services and support to SMEs. Devoting more than half of its human (700 people including 400 engineers) and technical resources to innovation, CETIM organizes its R&D in four areas: manufacturing processes and materials science, design-simulation-testing loop, sustainable development and expertise in controls and measurements. www.cetim.fr CIRAD The Centre de Coopération Internationale en Recherche Agronomique pour le Développement is the French organization for agricultural research and international cooperation for the sustainable development of the tropical and Mediterranean regions. Its activities are in the life sciences, social sciences and engineering sciences applied to agriculture, food, the environment and land management. It works on major themes such as food security, climate change, natural resource management, inequality reduction and poverty reduction. www.cirad.fr CNRS The Centre National de la Recherche Scientifique is a public research organization. Placed in France under the supervision of the Ministry of Higher Education, Research and Innovation, it produces knowledge and puts it at the service of society. Present throughout France, CNRS’s 32,000 researchers work in all fields of knowledge, in the organization’s 1,100 research and service units. Physicists, mathematicians, computer scientists: many CNRS researchers contribute to the

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development of digital simulation and its applications for the benefit of this scientific community. CNRS was created in 1939 at the initiative of Jean Zay (1904–1944), Minister of National Education and Fine Arts in the Popular Front government, assisted by Irène Joliot-Curie (1897–1956) and Jean Perrin (1870–1942), Nobel Prize winners in Chemistry and Physics in 1935 and 1926, respectively. It is one of the first global research organizations whose contributions cover both fundamental knowledge – an instrument of scientific sovereignty that is useful to all citizens – and its applications to the economic innovation of France and its partners. www.cnrs.fr DGA The Direction Générale de l’Armement is a department of the French Ministry of the Armed Forces whose main mission is to prepare the future of France’s defense systems. Within its technical department, various centers of expertise contribute to the development of digital simulation techniques. It supervises engineering schools, some of whose research laboratories are contributors to current innovations in numerical simulation. It participates in the financing of research organizations such as ONERA, CEA and CNES. www.defense.gouv.fr/dga ESA The European Space Agency is the third largest space agency in the world after NASA and the Russian Federal Space Agency. It is an intergovernmental space agency that coordinates space projects carried out jointly by some 20 European countries. Founded in 1974, ESA coordinates the financial and intellectual resources of its members, and can thus conduct space programs or develop scientific activities beyond the possibilities available, alone, to any European country. Supporting Europe’s space projects, ESA also ensures that investments in this field contribute to European citizens and humanity as a whole, collaborating with many space agencies around the world. ESA’s research programs aim to produce knowledge about the Earth and its near-space environment, our solar system and the Universe. ESA’s scientific activities contribute to the development of services offered by satellite technologies and support European industries.

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Scienntists, engineers, informattion and com mmunication technology t sppecialists, administtrative staff: ESA’s E teams consist c of abou ut 2,200 people representinng each of the mem mber countries.. ESA has an annuaal budget of €5.75 € billion, consolidated c b the contribbutions of by each meember countryy in proportioon to its GDP (this budget represents ann average annual contribution off around €20 for f the citizens of the membber countries).

a) On De ecember 4, 20 018, Ariane 5 lifted l off from m Europe’s Spa aceport in French Guiana and a delivered two satellites into their planne ed orbits

b) ES SA astronaut Thomas T Pesqu uet in the airllock during hiss first spacewa alk, on Friday January 13, 2017 7

Figure G.1. For its memb ber countries, ESA E is a gateway to space

COMMEN NT ON FIGUR RE G.1.– As tourist spac ce travel proojects are deeveloping [DAV 188, CAV 18], the experiencce of going in nto space, for example abboard the internatiional orbital station, remaains to this day d the priviilege of extraaordinary personallities. It mobillizes substantiial financial resources, r acccompanying a range of techniquues operated by b a human chhain with multiple skills [MO ON 17]. ww ww.esa.int GENCI The Grand Équipeement Nationaal de Calcul Intensif I is a French F public company b the Ministryy of Higher Education, E Ressearch and Innnovation, the CEA and owned by the CNR RS. It was created in 2007 2 by the French goveernment and aims to democraatize the use of computer simulation and a intensive computing too support French competitivene c nd industry. ss in all fieldss of science an GEN NCI provides powerful p com mputers (more than 5 Pflop/ss) for French scientists to carry out advancedd work that reqquires the usee of digital sim mulation. In adddition, it o three missiions: carries out

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– bringing the national strategy for equipping the national scientific community with intensive computing resources; – promote the use of numerical simulation and intensive computing, in particular for SMEs; – to participate in the creation of an integrated ecosystem for intensive computing on a European scale. www.genci.fr INRA The Institut National de la Recherche Agronomique is a French public institution of a scientific and technological nature. Under the dual supervision of the Ministry of Research and the Ministry of Agriculture, it is the leading agricultural research institute in Europe and the second largest in the world in agricultural sciences. Founded in 1946 in response to a social demand, that of “feeding France” in the aftermath of the Second World War, INRA conducts research in the service of major social issues. They cover three highly intertwined areas: food, agriculture and the environment. Its ambition is to contribute to the development of an agriculture that is competitive, respectful of the environment, territories and natural resources, and better adapted to human nutritional needs, as well as to new uses of agricultural products. In the 21st Century, the objective is now to “feed the world sustainably”. INRA’s missions, like those of many public institutions, are multiple: – produce and disseminate scientific knowledge; – train in and through research; – inform public decisions; – contribute to innovation through partnership and transfer; – develop the European and national research strategy; – contribute to the dialogue between science and society. The study and in situ experimentation of agricultural practices is at the heart of INRA’s research (Figure G.2). It makes it possible to evaluate production methods and collect data that could be useful for the validation of simulation models.

Glossary of Terms

a) Sower in an experimental field, 1960s (source: © INRA)

293

b) Urban beekeeping on the roof of the INRA headquarters in Paris, in 2018 (source: © Christophe Maitre/INRA)

Figure G.2. Several decades of in situ experiments at INRA

INRA is located in France in 17 regional centers where just over 8,150 employees (researchers, engineers, technicians, etc.) work in the fields of life sciences, material sciences and human sciences. www.inra.fr INRIA The Institut National de Recherche en Informatique et Automatique is a French public research institution dedicated to digital sciences. It promotes scientific excellence in the service of technology transfer and society. INRIA’s 2,600 employees explore original techniques with its industrial and academic partners. INRIA thus responds to the multidisciplinary and applicative challenges of the digital transition. At the origin of many innovations that create value and employment, it transfers its results and skills to companies (start-ups, small and medium-sized enterprises and large groups) in areas such as health, transport, energy, communication, security and privacy, the smart city and the factory of the future. INRIA was created in 1967 as part of the Plan Calcul [MOU 10]. A French government strategy decided by Charles De Gaulle at the initiative of a group of senior civil servants and industrialists, the plan was designed at the time to ensure France’s autonomy in information technologies and to develop a European IT system. www.inria.fr

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IFREMER The Institut Français de Recherche pour l’Exploitation de la Mer is a French public institution under the supervision of the Ministry of Ecology, Sustainable Development and Energy and the Ministry of Higher Education, Research and Innovation. The Institute’s research supports the deployment of the French State’s maritime policies, the Common Fisheries Policy of the European Union and national biodiversity strategies. IFREMER’s research and expertise contribute to: – know, assess and develop ocean resources and enable their sustainable use; – improve methods for monitoring, forecasting, evolution, protection and enhancement of the marine and coastal environment; – promote the economic development of the maritime world. IFREMER designs and implements observation, experimentation and monitoring tools, and manages oceanographic databases. www. ifremer.fr IFSTTAR Placed under the joint supervision of the French Ministry for the Ecological and Solidary Transition and the Ministry of Higher Education, Research and Innovation, the Institut Français des Sciences et Technologies des Transports, de l’Aménagement et des Réseaux is a French public scientific and technological institution. IFSTTAR conducts finalized research and expertise in the fields of transport, infrastructure, natural hazards and the city to improve the living conditions of citizens and more broadly to promote the sustainable development of societies. Its missions are carried out, in particular, for the benefit of the services of the line ministries, other administrations and bodies attached to them, local authorities, European and international institutions, professional associations, companies and users’ associations. www.ifsttar.fr

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295

IRT The Instituts de Recherche Technologique are intended to support an industrial innovation strategy in promising markets for French companies. Their purpose is to support long-term partnerships between higher education and research institutions and companies. Spread throughout France, the eight IRTs (created by the French government in 2010) address cutting-edge techniques (Table G.1), including the digital engineering of the systems of the future, carried out in the Paris region by the IRT System-X. IRT

Location

Technical field

BIOASTER

Paris, Lyon

Infectious diseases and microbiology

B-Com

Rennes

Images and digital technologies

Jules Verne

Nantes

Structural production technologies (composite, metal and hybrid)

M2P

Metz, Belfort

Materials, processes and metallurgy

NanoElec

Grenoble

Nanoelectronics

Railenium

Lille

Railway infrastructure

Saint-Exupéry

Bordeaux, Toulouse

Aeronautics, space and embedded systems

System-X

Saclay

Digital engineering of the systems of the future

Table G.1. The eight French IRTs cover advanced technical fields and are distributed throughout the national territory (Data: Ministère de l’Enseignement Supérieur, de la Recherche, et de l’Innovation in France, http://www.enseignementsup-recherche.gouv.fr/)

NAFEMS NAFEMS (National Agency for Finite Element Methods and Standards), a not-for-profit organization established in 1983, is the International Association for the Engineering Modeling, Analysis and Simulation Community. NAFEMS aims to establish best practice in engineering simulation and improve the professional

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status of all persons engaged in the use of engineering simulation. It provides a focal point for the dissemination and exchange of information and knowledge relating to engineering simulation, and also acts as an advocate for the deployment of simulation. NAFEMS promotes collaboration and communication between communities of industrial and academic practitioners of numerical simulation, by continuously improving the education and training in the use of simulation techniques. It is today recognized as a valued independent authority that operates with neutrality and integrity. NAFEMS focuses on the practical application of numerical engineering simulation techniques, such as the Finite Element Method for Structural Analysis, Computational Fluid Dynamics and Multibody Simulation. In addition to end users from all industry sectors, NAFEMS’ stakeholders include technology providers, researchers and academics. www.nafems.org NASA Created on July 29, 1958 by Order-in-Council of US President Dwight D. Eisenhower (1890–1969), the National Aeronautics and Space Administration is a government agency responsible for executing the US civil space program. It integrates all US scientific and technical expertise, including that of NACA, the US federal agency responsible for aeronautical research since 1915. In the context of military supremacy and technical rivalry between the USSR and the USA, the launch of Sputnik-1, the first artificial satellite in history, succeeded a few months earlier by the Soviets, caused a real shock in the USA. The creation of NASA meets the US objective of closing the gap in space control. The lunar program, announced by US President J.-F. Kennedy (1917–1963) in 1961, led to NASA’s real expansion. In the same year, on April 12, 1961, cosmonaut Yuri Gagarin (1934–1968) was the first man in space, followed by astronaut Alan Shepard (1923–1998) on May 5, 1961. The US made its first successful flight into orbit a year later, when astronaut John H. Glenn (1921–2016) made three revolutions around the Earth aboard Mercury Friendship 7. After flying nearly 130,000 kilometers in space over the 4 hours and 56 minutes of flight, the capsule landed in the sea east of the Bahamas, close to the point calculated by NASA engineers. This long-awaited American success is recounted in the films The Right Stuff [KAU 89] and Hidden Figures [MEL 16], among others.

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The latter evokess the personalities of Marry Jackson (11921–2005), K Katherine B women gifted in scieence, they Johnson and Dorothyy Vaughan (19910–2008). Black contributted to NASA’’s programs inn the 1960s, att a time when racial segregaation was being foought by persoonalities comm mitted to the struggle for equal rights aand when the best interests of sppace programss required the talents of everyone.

Figure e G.3. The tecchnical and sciientific contrib butions of Maryy Jackson, Ka atherine Johnson and Doroth hy Vaughan were w recounted d in the film Hiidden Figures (2016)

COMMEN NT ON FIGURE E G.3.– The work on aero odynamics doone by engineeer Mary Jackson is a direct contribution to numericall simulation as a we know it today. Mathemaatician and enngineer Katheerine Johnson n helped to calculate the traajectories and launnch windows of o many spacee flights – usin ng the methodd developed byy Euler to solve diifferential eqquations. Maathematician Dorothy Vauughan speciaalized in computeer science andd programminng in FORTR RAN, one of the t languagess used to develop the first layyers of computational cod de. Hidden Figures F whichh is both entertainning and thouught-provokingg, covers topiccs as diverse as the place oof women in sciencce, the role off humans in maajor engineerring projects and a changes inn societal attitudess (portraits of Mary Jacks kson, Katherin ne Johnson and a Dorothy Vaughan drawn byy Zelda Bombba). The US space connquest was acccomplished at the cost off technical annd human s test piloots and astronaauts paid the ultimate price for the spacce dream. risks – some Human spaceflight s is the hallmark of the US, reemaining NASA’s main acctivity for many yeears and accouunting for a siggnificant porttion of its annuual budget (onn average $8 billioon each year)). It suffered painful failu ures from thee beginning, with, for example, the death off the three members of the first Apollo mission: m Rogerr Chaffee d Ed White (1930–1967) died on (1935–1967), Virgil Grissom (1926–1967) and c on th he launch pad of the rockett that was January 17, 1967 in a fire in their capsule,

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to propel them to the Moon. In 2011, the United States ceased the space shuttle program. Two major accidents probably contributed to this decision: the take-off explosion of the Challenger shuttle on January 28, 1986 and the disintegration of Columbia on its return to the atmosphere on February 1, 2003, after a 16-day mission. 13 astronauts and a teacher, a passenger on the Challenger flight, died in these two accidents. The first is attributed to the failure of a seal on a thruster, the second to a defect in the beam heat shield. NASA carries out space and aerospace exploration and research missions by various means: probes, satellites, robotic missions, etc. On April 24, 1990, space shuttle Discovery launched the Hubble telescope, named in memory of US astronomer Edwin Hubble (1889–1953), to observe the Universe from space. Despite technical difficulties encountered at the beginning of its commissioning, this orbital observatory provides scientists with data that allows them to better understand how the Universe works. Current missions include the Mars Exploration Rover Discovery program, helping to uncover the secrets of the Red Planet (Figure G.4): on November 26, 2018, the InSight probe landed on Mars [MAL 18]. Earlier in 2018, NASA unveiled its plans for human exploration of the Moon and the Martian system. It published a calendar of assembly and logistics missions and manned missions, with the ambition of going to Mars in the 2030s.

Figure G.4. NASA’s robot on the ground on Mars

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COMMENT ON FIGURE G.4.– A self-portrait of NASA’s Curiosity Mars rover shows the robot at a drilled sample site called Duluth on the lower slopes of Mount Sharp. A Martian dust storm reduced sunlight and visibility in the Gale Crater. The northnortheast wall and rim of the crater lie beyond the rover, their visibility obscured by atmospheric dust (source: https://marsmobile.jpl.nasa.gov/). NASA, which also has a science department dedicated to studying the effects of climate change, employs about 20,000 people in 20 institutions, such as the Goddard Space Flight Center, the Jet Propulsion Laboratory, the Langley Research Center and the Kennedy Space Center. Scientific computation as a whole is one of the major techniques contributing to all NASA space projects, as well as to other global space agencies. In a context of strong economic and scientific rivalry between the US, China and other emerging countries, NASA is once again becoming the voice of the US ambition to send men to the Moon [MIN 19]. On January 2, 2019, China succeeded in placing a probe exploring the hidden side of the Earth’s satellite [JON 19, WAL 19]. On February 22, 2019, Israel flew into space with the objective of placing a probe on the Moon. The project, led by a non-governmental agency [HOL 19], would have cost less than $100 million [CLA 19] and ended in failure [CHA 19]. www.nasa.gov NOAA The National Oceanic and Atmospheric Administration is a US scientific agency within the United States Department of Commerce. It focuses on the conditions of the oceans, major waterways and the atmosphere. NOAA warns of dangerous weather, charts seas, guides the use and protection of ocean and coastal resources, and conducts research to provide understanding and improve stewardship of the environment. NOAA plays several specific roles in society, the benefits of which extend beyond the US economy and into the larger global community: – NOAA supplies its customers and partners with information pertaining to the state of the oceans and the atmosphere. This is clear through the production of weather warnings and forecasts via the National Weather Service, but NOAA’s information products extend to climate, ecosystems and commerce as well; – NOAA is a steward of the US coastal and marine environments. In coordination with federal, state, local, tribal and international authorities, NOAA

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manages the use of these environments, regulating fisheries and marine sanctuaries as well as protecting threatened and endangered marine species; – NOAA is intended to be a source of accurate and objective scientific information in the four particular areas of national and global importance identified above: ecosystems, climate, weather and water, and commerce and transportation. The main activities of NOAA are monitoring and observing Earth systems with instruments and data collection networks; understanding and describing Earth systems through research and analysis of that data; assessing and predicting the changes of these systems over time; engaging, advising and informing the public and partner organizations with important information; managing resources for the betterment of society, economy and environment. www.noaa.gov ONERA The Office National d’Études et de Recherches Aérospatiales is a French public establishment of an industrial and commercial nature. It has nearly 2,000 employees contributing to its missions, which aim to: – develop and direct research in the aerospace field; – design, carry out and implement the necessary means to conduct this research; – ensure (in liaison with the departments or bodies responsible for scientific and technological research) the national and international dissemination of the results of such research, encourage their exploitation by the aerospace industry and possibly facilitate their application outside the aerospace sector. ONERA has a fleet of wind tunnels contributing to the qualification of simulation methods and aircraft prototypes. It was created in the aftermath of the Second World War by decree of Charles Tillon (1897–1993), then French Minister of Armaments. ONERA has contributed to the implementation of many French industrial programs: Concorde or Airbus civil aircraft, Ariane rockets – to name the most prominent. www.onera.fr

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Abbreviations CFD Computational Fluid Dynamics (CFD) simulation involves using a computational code to solve the equations governing the flow of a fluid, which is also described by its law of behavior and the volumes in which it flows. The finite volume technique is the most commonly used in CFD for applications of interest to engineers. CSD The simulation of structural dynamics (Computational Structural Dynamics – CSD) consists of using a computational code that takes into account the geometry of the system under study, mathematical laws that translate the mechanical behavior of the materials of which it is made, and solving the equations of motion. Finite element technology is the most widely used in CSD for applications of interest to engineers. DNS The Direct Numerical Simulation (DNS) of flows consists of solving the conservation equations describing a turbulent fluid flow using a numerical method. FSI Fluid–Structure Interaction (FSI) refers to the exchange of mechanical energy between a vibrating structure and a fluid; the latter can be stagnant or in flow. In the first case, the interaction results in inertial effects for the structure, to which rigidity and dissipation effects can be added, depending on the frequency range considered. The latter are represented by means of added mass, stiffness and damping operators, which can be calculated numerically or analytically. In the second case, the interaction results in a transfer of energy from the flow to the structure, which can lead, for example, to vibration instability. FVM The Finite Volume Method (FVM) is a numerical method based on the writing of a conservation balance of a given physical quantity on a set of elementary volumes constituting the mesh of a domain in which a fluid flows, for example. The balance states that the variation of a quantity in a volume is the difference between the inflows and outflows in that volume. The method is widely used in fluid dynamics calculation codes.

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HPC High Parallel Computing (HPC) aims to use supercomputers (computers with outstanding computing performance) in order to perform simulations that require significant computing time. This computing power is used, for example, in the fields of meteorology, climatology and fluid mechanics, particularly for turbulent flows. The basic sciences (astrophysics, physics, chemistry) are among the main users of HPC computing resources. LBM The Lattice Boltzmann Method (LBM) is a fluid dynamics method. By solving Boltzmann’s discrete equation, it simulates the behavior of Newtonian and nonNewtonian fluids on a “mesoscopic” scale. At this scale of description, the fluid is described as a set of particles whose dynamics is rendered by the Boltzmann equation. The latter proposed it based on the work of Bernoulli and Maxwell. A distribution function models the kinetics of fluid particles. Depending on the time, position and velocity of the particles, its evolution is described by a “transport equation”: +

∙∇ = ( , , )

The first term of the first member describes the unsteadiness of the flow, the second term advection, reflecting the fact that particles move at a constant speed between two collisions. The second member reports collisions between particles; these are rendered using different shock models. In the LBM, the equation is solved using a collision-propagation scheme, allowing complex fluid behaviors to be reproduced. LES Large Eddy Simulation (LES) is a method of calculating flow to solve some of the turbulent scales (the large scales) and to model the influence of the smaller ones. RANS Reynolds Average Numerical Simulation (RANS) methods solve turbulent flow equations in the sense of an average, separating the evolution of the mean velocity and pressure fields from the contribution of fluctuations around this average. SPH The SPH (Smoothed Particle Hydrodynamics) method is a flow simulation method. Based on the description of the movement of fluid particles monitored in their evolution, it makes it possible to represent physical phenomena that are

Glossary of Terms

303

inaccessible to simulaation methodss using a calcculation of theeir velocity oon a fixed mesh. Itt was developped in the latte 1970s in astrophysics too simulate phhenomena such as the t formation and evolutionn of stars and galaxies. It thhen underwennt a major expansioon through its application inn fluid dynam mics, being appplied to the caalculation of comprressible, incom mpressible and multiphase flows. Technic cal terms Algorith hm An algorithm a is a procedure describing, usin ng a specific sequence of ellementary operationns (arithmeticc or logical), a systematic approach to solving a prroblem or performiing a task in a given numbeer of steps. We use u algorithm ms in our daily lives: wh hen followingg a recipe, orr a route proposedd by our navvigation system m or applicattion (Figure G.5), or by m making a purchasee on the Internnet. Algoorithms are beecoming increeasingly impo ortant, particullarly in their ability to perform complex calcculations, storre and transm mit information and learn ffrom data [ABI 17]].

F Figure G.5. An algorithm in our daily livess: cho oosing your me etro route (Source: www.rattp.fr)

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Artificial intelligence Artificial intelligence (AI) refers to all the theories, models, and numerical and algorithmic techniques used to produce machines capable of simulating (in the sense of reproducing) human intelligence. To draw up a complete panorama of it goes far beyond the scope of this book. Also, the examples to which we refer here are mainly those of machine learning.

Figure G.6. AI nowadays corresponds to a set of concepts and techniques rather than an autonomous discipline (source: www.123rf.com)

Many algorithms can be implemented in machine learning, particularly depending on the objectives assigned to the AI and the data available. In this book we discuss one of the most well-known techniques, that of neural networks. The term artificial intelligence first appeared at a conference dedicated to this technique, organized in the 1950s by American computer scientists John McCarthy (1927–2011) and Claude Shannon (1916–2001). At that time, when the best minds were wondering about the possibility of building thinking machines, Alan Turing proposed a test to determine if a machine showed “intelligence”. The device he imagined is as follows. A human interrogator, interacting with two entities without seeing them, must determine which one is the human and which one is the machine. If he is mistaken more often than when he has to distinguish (in the same circumstances) a woman from a man, then the machine passes the test. The Turing test is first of all valid for the empirical purpose it assigns to AI – to make the

Glossary of Terms

305

machinee’s performancce rival that off a human in different d regissters deemed tto require intelligennce. For morre than 50 yeears, Turing’ss questions abbout the posssibility of building thinking macchines have coontinued to stimulate the AII research com mmunity. Big Dataa Big Data D refers too a set of tecchniques aimeed at collectinng and storingg data of various kinds, availabble in large quantities q and d sometimes in a fragmennted way. Algorithhms for processsing these daata aim in partticular to estabblish the linkss between these daata (Figure G.7), G in orderr to propose models that make predicttions and contributte to decision support. Data is the raw maaterial of Big Data, as well as calculationns performed in digital H havving a lot of ddata is not simulatioon or artificiaal intelligence algorithms. However, enough! In particular, developing predictive mo odels requiress the use of sstructured o system. databasees that synthessize the expertts’ knowledgee of a subject or On physical p systeems, data cann come from experimental devices, oppportunity measurem ments (airplanne in flight, shhip at sea, etcc.) and numeriical simulationns, which allow a broad b operatioonal domain too be explored at a lower cosst and risk. Annootating raw data d (images,, sounds, tex xts, physical signals, etc.), that is, linking it i to a contextt in order to give g it meanin ng, is thus onne of the challlenges of Big Dataa: data acquirees greater valuue for predictiive use.

Figure G.7. Relation nships between n data of different kinds rep presented in th he graph ource: www. commons.wiki c imedia.org). For F a color verssion of this fig gure, see form (so www.iste.co o.uk/sigrist/sim mulation2.zip

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Blockchain Blockchain is a technique for storing and transmitting information. Known as transparent and secure, it operates without a central control system. The blockchain implementation contributes to the increased demand for data processing and storage. A blockchain is a database containing the history of all exchanges between its users since its creation. The blocks contain transactions, writing operations performed in a specific order. Shared by its various users, without intermediaries, this database is secure and distributed. This allows everyone to check the validity of the chain. The uses of the blockchain are potentially varied. For example, it contributes to the transfer of assets (currencies, securities, votes, shares, bonds, etc.) and improves their traceability. It allows smart-contracts, autonomous programs that automatically execute the terms and conditions of a contract, without requiring human intervention once they have started. The fields of exploitation of the blockchain are numerous, particularly in sectors requiring transactions (banking, insurance and real estate), data exchanges (pharmaceutical and artistic industries) or product exchanges (agri-food, aeronautics and automotive industries).

Figure G.8. Blockchain operating principle (source: www.123rd.com)

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307

COMMENT ON FIGURE G.8.– The operation of the blockchain is schematically as follows. A user (A) makes a transaction to another user (B). This, like all transactions carried out by users, is distributed on different nodes of a network that ensures validation according to techniques and algorithms depending on the type of blockchain. Once the block is validated, it is time-stamped and added to the block chain. The transaction is then visible to the receiver and the entire network. The decentralized nature of the blockchain, coupled with its security and transparency, promises much broader applications than the monetary field in which, with Bitcoin, it has emerged (source: https://blockchainfrance.net). Computer data Representation of information in a program: either in the program text (source code) or in memory during execution. The data, often coded, describes the elements of the software such as an entity (thing), interaction, transaction, event, subsystem, etc.1. Datum/data – What is known or accepted as that, on which to base a reasoning, which serves as a starting point for research (especially plural) – Current biological data. – A fundamental idea that serves as a starting point, an essential element on which a book is built – The data of a comedy. – Intelligence as a basis (especially plural) – Lack of data for in-depth analysis. Data corresponds to an elementary description of a reality: for example, an observation or a measurement. It is devoid of any reasoning, supposition, recognition or probability. Unquestionable or undisputed, it can be used as a basis for research. It results from the processing of raw data, that is, data that has not been interpreted and comes from a primary source. The processing makes it possible to give it a meaning and thus to obtain information. Differential equation A differential equation has one or more mathematical functions as unknown. It takes the form of a relationship between these functions and their successive derivatives – their variations over time. Mathematicians write differential equations as follows:

1 According to Wikipedia: https://fr.wikipedia.org/wiki/Donnée_informatics.

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= ( , ) The left member of the equation represents the variation in time of a function and the right member represents a relationship between this function and time. Newton and Leibniz gave mathematical meaning to the writing of the derivative, which relates minute variations of two quantities (as expressed by the term of the first member of the equation). Differential equations were used to construct mathematical models of mechanics. For example, they make it possible to express the law of motion linking the acceleration of a body with the forces exerted on it (acceleration is the variation of speed, itself a variation of displacement). They also represent many physical phenomena (electricity, chemistry, heat, electromagnetism, etc.). They are also used to describe biological, chemical or demographic evolution processes, for example. The Lorenz equation (Chapter 1, first volume) and the Lotka–Volterra equations (Chapter 1, second volume) are examples of differential equations. The solutions of differential equations can be represented in different ways, for example by plotting the evolution of each of the components of ( ) as a function of time. In some cases, this process makes it possible to visualize a strange attractor, the set of points towards which a system evolves and the dynamics of which is represented by a differential equation: the arabesques obtained could compete with some artists’ creations (Figure G.9)!

Figure G.9. Visualization of strange attractors (source: http://www.chaoscope.org/gallery.htm). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

Disruption Disruption is a noun of Latin origin in which the prefix dis reinforces the intensity of the verb rumpere, to break. A disruption therefore refers to a sudden break. It is used in geology, for example, to refer to the mechanisms of cracking and

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309

dislocation of rock layers. Surprisingly enough, the word “disruption” has been turned into a registered concept for marketing purposes [CHR 15, NOR 16]! Disruption then refers to a so-called “breakthrough” innovation, one that challenges an established practice or market by offering a new good or service. The breakthrough innovation, promoted by the media, would be opposed to incremental innovation, presented as an improvement of a technique or practice. Equations An equation is a mathematical writing that translates a concrete problem or a physical (or other) principle into abstract language. Solving an equation consists of providing an answer to this problem. This makes it possible, among other things, to understand a physical phenomenon and/or to carry out different virtual experiments using computation. An equation works like a scale linking quantities separated by a symbol of equality. It involves unknown quantities to be determined. These depend on variable quantities and known data (parameters). The unknown of an equation can be a number (the purchase price of an object or service) or a more complex mathematical entity (e.g. a function, giving the evolution of one physical quantity as a function of another, such as the consumption of an automobile during a journey). Let us solve an arithmetic problem proposed by French writer Jean-Louis Fournier using an equation: A salmon leaves Saumur via the Loire at 9:30 am, and it reaches a speed of three knots. A second leaves Saumur at 10 am in the same direction. At what time will the second salmon, which is travelling at four knots, reach the first fish’s tail? [FOU 93] To answer this question, let us remember that distance is the product of speed and travel time. Let us count the latter from the time of the second salmon’s departure and note it t. The first salmon starts 0.5 hours ahead of the second and wims at a speed of 3 knots; the second catches up with it at a speed of 4 knots. The distance between them is then calculated as t + 0.5 × 3 − 4 × t. It is nil when: ( + 0.5) × 3 − 4 × = 0 We have written an equation that enables us to answer the question. This one has as unknown the travel time and as parameters the swimming speeds (3 and 4 knots), as well as the advance of the first salmon (0.5 hours). We solve the equation using basic algebraic rules and we determine:

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= 0.5 ×

3 = 1.5 4−3

This allows us to answer the question posed: the second salmon catches up with the first an hour and a half after leaving, at 11:30 am. Finite element method The finite element method is used to solve partial differential equations numerically. It appeared at the end of the 19th Century, particularly with the work of Maxwell. Known for his contributions to electromagnetism, he is also the precursor of the finite element method. The latter then developed with the need to analyze the structures and strength of the materials they use. The first studies in this field were carried out in particular by: – Carlo-Alberto Castigliano (1847–1884), an Italian engineer and mathematician, who was interested in the mathematical theory of elasticity and the mechanics of deformable structures; – Christian Otto Mohr (1835–1918), a German mechanical engineer known for his contributions to the mechanics of materials. In particular, he has developed a calculation method representing the state of stress in a solid. These scientists used equations solved analytically, using hand-operated calculations. The mathematical formalization of the finite element method was carried out later, around the middle of the 20th Century. Various mathematicians and engineers contributed to its industrial development, in particular Olek Cecil Zienkiewicz (1921–2009), a Welsh engineer, who devoted most of his scientific life to supporting its development in different fields of modern mechanics [ZIE 67].

Figure G.10. Stress calculation in a mechanical part with the finite element method (source: EC2 Modélisation, www.ec2-modelisation.fr). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

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311

Numerical calculation combined with high-performance computer-based resolution techniques nowadays ensures the generalization of the method in many technical fields. Modeling Modeling is using mathematics to represent the world or some of its particular aspects. Abstract objects play the role of real objects and from knowledge of them it is hoped that we can draw an understanding of the world. When the modeling is correct, the study of the mathematical model provides information on the situation, object or structures that the model targets. Under these conditions, it can be used for virtual experiments: testing theoretical hypotheses, checking the functioning of a system, ensuring its reliability, trying to anticipate a phenomenon, etc. Model reduction Model reduction methods have been a significant innovation in scientific computation in recent years. They have helped to make the practice evolve towards greater efficiency without losing any precision. Industrial numerical simulations very often use models with a large number of unknowns. They are interested in very large systems that require calculations over long periods of time and that take into account a multitude of physical parameters. Model reduction methods are receiving increasing attention from the industrial world, which is using them more and more systematically. In mathematical terms, reducing a model consists of retaining from a complete model (containing all the information necessary to describe the system under study) only the contributions of certain quantities, those that are most relevant for the desired solution of the problem. The reduced-order model thus obtained contains information that is incomplete but sufficient to describe the overall behavior of the object. It is just like in a recording of a concert where it would be a question of keeping only the contribution of the major instruments – and also correct the missing contribution so as not to disturb music lovers’ ears! This is like moving from a written problem to a large matrix (several hundred thousand unknowns):

Ax = b to a similar problem, written on a matrix of small size, or even very small size (several tens of unknowns): A x =b Rating with the index indicates that the matrices used in the calculation are constructed from the vibration modes. In some cases, the reduction can be

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significant: from a model containing tens of thousands of degrees of freedom (or unknowns), it is possible to build a model reduced to only a few tens of unknowns! Numerical simulation A numerical simulation is a series of calculations performed on a computer to reproduce a physical phenomenon. It leads to a description of how this phenomenon unfolded, as if it had actually occurred. A numerical simulation can represent complex physical phenomena and is based on a mathematical model with equations. Partial differential equation A partial differential equation involves the variations (derivatives), in time and space, of a given physical quantity, depending on time variables (noted ) and space variables (noted , in two dimensions). The derivatives in question may be noted

,

(first and second order derivatives with respect to time),

order derivatives with respect to each of the space variables) and

,

(first

,

(derivative of the second order in space), etc. Partial differential equations are found in many mechanical (solid, fluid) or electromagnetic models: the d’Alembert or Schrödinger equations (Chapter 1, first volume), the Maxwell equation (Chapter 2, first volume) or the Navier–Stokes equations (Chapter 2, second volume) are examples of partial differential equations. Personal data Information concerning ethnic origin, political, philosophical or religious opinions, trade union membership, health or sex life. In principle, sensitive data can only be collected and used with the explicit consent of the individual(s) concerned2. R&D Research and development (R&D) encompasses creative work undertaken systematically to increase the amount of knowledge available to human communities (companies, communities, states) and the use of this amount of knowledge to develop new applications. R&D work exclusively includes the following activities: – basic research. This is undertaken either out of pure scientific interest (it is basically free research) or to make a theoretical contribution to the solution of

2 According to the Commission Nationale de l’Informatique et des Libertés: http://www.cnil.fr.

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313

technical problems (it is fundamental research oriented towards application and possibly commercial purposes); – applied research. This aims to identify possible applications of the results of fundamental research or to find new solutions to achieve a specific objective chosen in advance; – experimental development. This is based on knowledge obtained through research or practical experience and is carried out using prototypes or pilot installations to launch new products, establish new processes or substantially improve existing ones. While the expenses incurred by these various communities to carry out this work are often presented as costs, they contribute above all to their future-oriented development. Part of this investment is assumed by the citizens themselves, thus participating in the research effort of the communities to which they belong. In OECD countries, in 2016, the number of researchers represented just over 4.5 million full-time equivalent jobs – including nearly 2 million in the European Union (Table G.2). Country

Number of employees

Private research

Public research

Germany

400.812

59%

41%

China

1.492.176

62%

38%

South Korea

361.292

80%

20%

United States

1.379.977

70%

30%

France

284.766

60%

40%

Japan

665.566

73%

27%

United Kingdom

291.416

38%

62%

Sweden

70.372

67%

33%

European Union

1.889.183

49%

51%

OECD

4.770.739

60%

40%

Table G.2. The number of researchers in different OECD countries in 2016: full-time equivalent jobs, share of researchers in companies and public research (Data: Ministry of Higher Education, Research and Innovation in France/http://www.enseignementsup-recherche.gouv.fr/)

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Figure G.11. Global R&D investment in 2018 (source: How Much?, https://howmuch.net). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE G.11.– The world’s major economies devote a significant share of their wealth to R&D investment. The research effort can be assessed by considering the ratio between the wealth produced annually by a country and the total amount of investment. This ratio is 2.34% for the OECD as a whole (2.22% for France). In 2018, the United States remained the largest investor in R&D, with just over $475 billion, followed by China ($370 billion) and Japan ($170 billion). The 28 countries of the European Union together invested nearly 350 billion dollars. The two largest investors are Germany (110 billion) and France (60 billion). On average in OECD countries, public research accounts for nearly 30% of total R&D expenditure, including 35% in France (source: Ministry of Higher Education, Research and Innovation in France, http://www.enseignementsup-recherche.gouv .fr/). Virtual and augmented reality Virtual reality refers to a set of techniques and systems that give humans the feeling of entering a universe. Virtual reality gives the possibility to perform in real

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315

time a certain number of actions defined by one or more computer programs and to experience a certain number of sensations (auditory, visual or haptic for example). Augmented reality refers to a virtual interface, in two or three dimensions, that enriches reality by superimposing additional information on to it. Virtual or augmented reality also allows manufacturers to simulate operating conditions or machine assembly conditions, for example. These digital techniques make it possible, for example, to train operators in delicate operations and to carry them out with increased safety and ergonomics.

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Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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351

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[VER 87] VERHOEVEN P., RoboCop, 1987. [WAC 99] THE WACHOWSKIS, The Matrix, 1999. [WEI 98] WEIR P., The Truman Show, 1998. [WEN 11] WENDERS W., Pina, 2011. [WEN 14] WENDERS W., The Salt of the Earth, 2014. [ZAI 93] ZAILLIAN S., Searching for Bobby Fischer, 1993. [ZHA 07] ZHANGKE J., Still Life, 2007. [ZWI 14] ZWICK E., Pawn Sacrifice, 2014.

Index

3D printing, 81, 154, 203, 216, 245

B

A

Baekland, Leo, 151 Becquerel, Henri, 173, 174 bees, 263 Bernoulli, Daniel, 35, 36, 39, 302 Big Bang, 89, 92 Biot, Jean-Baptiste, 18 black holes, 89, 100, 102, 104–106 blood, 202, 211, 216–218, 220–223, 225, 226 circulation mechanism, 216–218 flow simulation, 222 Blue Marble, 133, 164 Bouly, Léon, 165 brain imaging, 209, 211, 214 science (neuro-science), 209, 214, 228, 229, 231, 232, 275 simulation, 230, 231

acoustics, 75, 258, 260 additive manufacturing, 60–63 Ader, Clément, 33 advection, 41, 47, 139, 302 affective computing, 275, 276 agriculture, 1, 7, 138, 164, 289, 292 aircraft, 33–36, 45, 47, 50, 70, 73–75, 109, 139, 150, 194, 213, 300 albedo effect, 160–162 ALE, 82, 83, 187 aneurysm, 223 angiogenesis, 218 Argo floats, 148, 149 Aristotle, 201 artificial intelligence, 10, 28, 104, 214, 232, 235, 270, 271, 278, 284, 304, 305 astrophysics, 87–89, 105–107, 113, 302, 303 atmosphere, 18, 19, 24, 99, 105, 127, 133, 135–141, 144, 147, 155–157, 160–162, 244, 256, 258, 260, 298, 299 augmented reality, 59, 60, 314, 315 axon, 230

C Cayley, Georges, 33 CERFACS, 74, 140, 159, 288 CETIM, 56, 289 CIRAD, 26, 289 CO2, 23, 24, 135–137, 145, 148, 155, 156, 162, 163, 175, 217 cobot, 59

Numerical Simulation, An Art of Prediction 2: Examples, First Edition. Jean-François Sigrist. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

354

Numerical Simulation, An Art of Prediction 2

combustion, 50–53, 76, 81, 107, 168– 172, 295 composite, 51, 53, 76, 81, 295 conservation, 39, 41, 45–47, 74, 105, 109, 129, 186, 301 energy, 46, 74, 108, 170 mass, 105 momentum, 46, 74 convection, 19, 41, 150, 181 Copernicus, Nicolaus, 95 corrosion, 76–78 Coulomb, Charles-Augustin, 260, 261, 262 Courant-Friedrich-Lewy condition, 144 Crick, Francis, 212 CRISPR, 211 Curie, Irene, 174, 290 Curie, Marie, 174 Curie, Pierre, 174

D d’Arlandes, François-Laurent, 33 da Vinci, Leonardo, 40, 42, 83 Darcy, Henry, 18, 52 DART, 122 data assimilation, 140, 141, 147, 156 genomic, 214 learning, 6, 16, 28, 29, 36, 46, 59, 147, 247, 269, 275 medical, 204, 206, 214 debris, 117, 124–127 decision-making, 10, 11, 13, 241, 273, 284 demographic transition, 3 dendrite, 230 diffusion, 18, 19, 41, 47, 54, 135, 144, 208, 209, 218, 266, 269, 285 digital twin, 59, 213, 214 DNA, 211–213 molecule, 212

sequencing, 213 structure, 212 drone, 9 Duchenne, Guillaume-Benjamin, 275 dye, 41, 227, 228

E Earth magnetic field, 150 overshoot day, 4 earthquake, 114–123, 128 Edison, Thomas, 165 EEG, 209, 210, 234 Einstein, Albert, 98, 100, 101, 109 emotions, 119, 239, 243, 247, 272– 279 entropy, 171 equation(s) Navier-Stokes, 39, 41, 73, 74, 143, 147, 191 Newton, 94, 186 Schrödinger, 22, 312 eruption, 114, 115, 121, 123, 124, 126–131, 135 ESA, 97, 150, 151, 290, 291 Euler, Leonard, 39, 82, 83, 98, 186, 187, 265, 297 experiments “in silico”, 200, 201, 203 “in vitro”, 200, 201, 203 “in vivo”, 200, 201

F Facebook, 238 FACS, 274 FAO, 5, 6, 24 fertilizers, 12, 14, 16–20, 154 Feynman, Richard, 20 Fibonacci, Leonardo, 25 Fick, Adolf, 18

Index

finite element, 52, 69, 76, 215, 223, 224, 310 volume, 46, 47, 74, 197, 301 flow laminar, 41, 42 stationary, 126 turbulent, 41–45, 70, 72, 73, 75, 186, 302 unsteady, 73, 75 fluid-structure interaction, 187 Franklin, Rosalind, 212

355

J, K Julliot, Frédéric, 174 Kepler, Johannes, 95, 96 Kolmogorov, Andrey, 44

L

general relativity, 100, 101, 104, 109 genomic medicine, 213 geophysics, 87, 114, 116, 117 global warming, 135, 161, 164 Google, 238, 251, 252, 253 gravitation, 89, 90, 92–95, 97–105, 112 gravitational wave, 89, 101–105 greenhouse effect, 135, 160, 161

L-systems, 26, 27, 28 Lagrange, Joseph-Louis, 82 points, 99, 100 Lamb, Horace, 42 LBM, 73–75, 302 Leray, Jean, 47 LES, 45, 73, 161, 162, 182, 183, 191, 192, 194, 197, 253, 302 lexical statistics, 242 lifting force, 45 profile, 36, 70 LIGO, 103, 104 Lilienthal, Otto, 33 Lotka, Alfred-James, 7–9, 308 Lumière, Auguste, 165 Lumière, Louis, 165

H, I

M

Hahn, Otto, 174 Harvey, William, 216, 217 Hawking, Stephen, 100 heart, 200, 203, 204, 208, 217, 218, 226 digital model, 203 flow simulation, 222 HPC, 23, 49, 73, 113, 119, 188, 302 Hypatia, 96 IAEA, 175 indicator, 11, 13, 160, 258, 260 INRA, 7, 9, 10, 17, 292, 293 Interplanetary Transport Network, 100 inverse methods, 140 IPCC, 155, 158–160, 163 ITER, 184, 186

MEG, 209, 210, 211 MHD, 105, 186, 187 Miescher, Friedrich, 212 model biomechanical, 202, 225 elastic, 215 language, 270, 272 mathematical, 137, 203, 215, 227, 228, 258, 281, 308, 311, 312 mechanistic, 7, 11 meteorological global, 138, 139 local, 18, 139, 140 numerical, 6, 7, 15, 50, 52, 59, 61, 62, 66, 67, 69, 70, 76, 89, 105, 117, 125, 129, 130, 157, 159,

G

356

Numerical Simulation, An Art of Prediction 2

194, 213, 220, 225, 229, 250, 281, 282, 288 OCEAN, 247, 248 patient-specific, 214, 220 personality, 247 physical, 46, 90, 147, 156, 257 psychological, 248, 250 viscoelastic, 202, 215 Montgolfier, Jacques-Etienne, 33 Montgolfier, Joseph-Michel, 33 Mount Fuji, 120, 127, 128, 131 Mount Pinatubo, 128, 135 MRI anatomical, 207 diffusion, 208, 209 virtual, 222, 223

N N-body, 90 problem, 98 simulation, 93 NASA, 8, 23, 24, 99–102, 134, 135, 164, 290, 296–299 Nash, John, 239 Navier, Claude, 39, 41, 44, 45, 47, 48, 50, 73, 74, 82, 126, 143, 147, 186, 191, 196, 312 network, 4, 20, 52, 70, 73, 74, 90, 92, 93, 99, 122, 123, 140, 149, 217, 218, 223, 233, 241, 253–256, 264–268, 270, 272, 300, 304, 307 neuromorphic chip, 232 neuron, 209, 230, 231, 233, 234 NeuroSpin, 208–211 NOAA, 122, 123, 299, 300 Noether, Emmy, 109 noise, 46, 68–70, 73–76, 186, 256– 260 non-destructive testing, 56–58, 173 nuclear energy, 78, 173–175, 178, 188, 287

fission, 176 fusion, 174, 176

O ocean, 8, 24, 31, 32, 38, 39, 63, 69, 97, 105, 115, 121–125, 133, 135, 136, 144–153, 155–162, 164, 284, 294, 299 optimization, 61, 78, 79, 85, 141, 198 OuLiPo, 269 Overview Effect, 133, 164

P Pascal, Blaise, 87, 88 Pilâtre de Rozier, Jean-François, 33 plasma, 105, 107, 183–187, 217, 219 plastic debris, 152, 153 political community, 266, 267 psychological profile, 248, 250 PWR, 175, 178, 180

R Rabelais, François, 285, 286 RANS, 45, 72, 73, 191, 192, 194, 197, 302 Reynolds, Osborne, 42, 45, 302, 218 number, 42, 218 Richardson, Lewis, 44 robot, 58, 59, 204, 206, 232, 234, 245, 254, 276, 277, 279, 298, 299 robotic-assisted surgery, 204, 205 Röntgen, Wilhelm, 173, 174 Rutherford, Ernest, 174

S satellite, 8, 9, 23, 24, 97–99, 121, 134, 140, 147, 148, 150, 151, 290, 291, 296, 298, 299 scale-descent methods, 142, 143 sea-keeping, 63, 66

Index

Sénac, Jean-Baptiste, 201 SPH, 52, 113, 302 stability, 19, 63, 64, 78, 79, 83, 107, 110, 139, 194, 225 statistics, 18, 196, 242, 247, 251, 254 stent, 220, 223, 224, 226 Stokes, Gabriel, 39, 41, 44, 45, 47, 48, 50, 52, 73, 74, 82, 126, 186, 196, 312 Strassman, Fritz, 174 submarine, 33, 65, 69, 70, 77, 150, 178

T thermodynamics, 22, 52, 111, 112, 161, 165, 166, 170, 185 Thompson, d’Arcy, 24 tokamak, 185, 186, 187 tsunami, 114, 115, 120–125, 127 turbine gas, 171, 172 hydraulic, 70, 167, 190, 191 wind, 36, 44, 70, 171, 193–195, 197, 256, 258 turbulence average simulation (RANS), 45, 72, 73, 191, 192, 194, 197, 302 direct numerical simulation (DNS), 44, 45, 301

357

large eddy simulation (LES), 45, 73, 161, 162, 182, 183, 191, 192, 194, 197, 253, 302 turbulent excitation, 71–73 Twitter, 265, 267, 268, 269

U, V ultrasound, 56, 57, 206–208 Van Dyke, Milton, 44 virtual reality, 59, 60, 314 volcano, 123–131 Cumbre Vieja, 124, 126 Eyjafjöll, 128 Merapi, 130, 131 Scopoma, 127 Volterra, Vito, 7–9, 308

W, X, Y Watson, James, 212 Watt, James, 166 weather forecast, 133, 138, 155, 158 welding, 53–56, 61, 62 Wilkins, Maurice, 212 Wright, Orville, 33 Wright, Wilbur, 33 X-ray, 173, 174, 212 yield, 2, 4, 5, 7, 11, 13–16, 27, 28, 64, 100, 119, 191, 195, 197, 232

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