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1 Chapter 1Figure 1.1. Cereal harvest, Tomb of Menna, Sheikh Abd el-Gournah Necropolis, Egy...Figure 1.2. Allocation of land areas for food production (source: Our World in D...Figure 1.3. World population growth between 1750 and 2015 and projections to 210...Figure 1.4. Annual world wheat yields for 2014, expressed in tons per hectare. W...Figure 1.5. Although edible, these tomatoes, produced in France, are discarded b...Figure 1.6. How thirsty is our food? (source: https://www.statista.com/chart/948...Figure 1.7. Satellite image showing algae growth in a North Atlantic region (sou...Figure 1.8. Typical evolution of the prey/predator populations as predicted by t...Figure 1.9. Agricultural drones are used to monitor crops and collect useful dat...Figure 1.10. Share of production allowed by the ecosystem services associated wi...Figure 1.11. Working hours (per ha and per year) required by a farmer for “conve...Figure 1.12. Soya is a legume valued for its nutritional qualities and whose int...Figure 1.13. Calculation of wheat crop yields in France and worldwide: the figur...Figure 1.14. Fertilizers promote plant growth but their overintensive use has lo...Figure 1.15. Global use of nitrogen, potassium and phosphate fertilizers worldwi...Figure 1.16. From the use of nitrogen fertilizers to ammonia emissions in France...Figure 1.17. 3D representation of atrazine (source: www.commons.wikimedia.org). ...Figure 1.18. Example of calculation at the atomic scale [BEL 17b]. For a color v...Figure 1.19. Vegetation map obtained from satellite observations (source: NASA/w...Figure 1.20. The Fibonacci spiral: a model (too simple?) to explain plant growth...Figure 1.21. Variety of leaf shapes (source: www.123rf/Liliia Khuzhakhmetova)Figure 1.22. Weeds generated by a three-dimensional L-system program (source: ww...Figure 1.23. The virtual plants (left), obtained in silico by means of L-systems...

2 Chapter 2Figure 2.1. To which countries does the world export? (source: Observatory for E...Figure 2.2. Taken from the work of Édouard-Thomas de Burgues, Count of Missiessy...Figure 2.3. Visualization of maritime and air traffic. For a color version of th...Figure 2.4. Flow calculation around a lifting profile (source: Naval Group). For...Figure 2.5. Simulation of the aerodynamics of a sail (source: image owned by Tot...Figure 2.6. Simulation of possible routes for an offshore race (image made using...Figure 2.7. Chocolate is a non-Newtonian fluid (source: www.123rf.com/kubais)Figure 2.8. Old man contemplating the flow of water, drawing by Leonardo da Vinc...Figure 2.9. A flow from the laminar state (left) to the turbulent state (right) ...Figure 2.10. Observation by Osborne Reynolds on flows [REY 83]Figure 2.11. Triangular prism presenting one of its bases, Etienne-Jules Marey, ...Figure 2.12. Flow calculation around a bearing profile with turbulence resolutio...Figure 2.13. Examples of hydrodynamic calculations around a hull appendage (sour...Figure 2.14. Meshing of the fluid in finite volumes around an aircraft (source: ...Figure 2.15. Modal analysis of a flow [KAR 18]. For a color version of this figu...Figure 2.16. Calculation of water flow downstream of a cylinder with a reduced o...Figure 2.17. Simulation of the wave surge on a frigate (source: calculation carr...Figure 2.18. Example of a composite material: a multilayer (source: www.commons....Figure 2.19. Numerical simulation for composites: manufacturing processes and me...Figure 2.20. Welding operation (source: www123rf.com/Praphan Jampala)Figure 2.21. The thermal, mechanical and metallurgical phenomena involved in wel...Figure 2.22. Numerical simulation of welding (source: Naval Group). For a color ...Figure 2.23. Ultrasonic inspection of a welded part (source: 123rf.com/Jarawa Ja...Figure 2.24. Simulation of the control of a shaft by multielement ultrasound (le...Figure 2.25. Collaborative robot (source: © RB3D/www.rb3d.com)Figure 2.26. Ergonomics demonstration using virtual reality at the French instit...Figure 2.27. Thermomechanical numerical simulation of an additive manufacturing ...Figure 2.28. Additive manufacturing of a real part: numerical simulation with th...Figure 2.29. Stability study of a ship, carried out with the MAAT-Hydro calculat...Figure 2.30. Analysis of sea-keeping (source: Sirehna/Naval Group). For a color ...Figure 2.31. Numerical model of a ship with stabilizer fins [YVI 14]. For a colo...Figure 2.32. Simulation of wave resistance [YV1 14]. For a color version of this...Figure 2.33. Numerical simulation of ship vibrations: example of acoustic radiat...Figure 2.34. Numerical model of a suspension mount [PET 12]. For a color version...Figure 2.35. Development of a turbulent boundary layer on a wallFigure 2.36. Empirical spectra of turbulent excitation [BER 14]. For a color ver...Figure 2.37. Numerically calculated and empirically determined turbulent excitat...Figure 2.38. The calculation grid used in the Lattice Boltzmann Method can be ad...Figure 2.39. Flow simulation on an aircraft using the Lattice-Boltzmann method (...Figure 2.40. Simulation helps to understand the evolution of corrosion. For a co...Figure 2.41. Modeling of a corrosion protection system for a ship’s hull (source...Figure 2.42. Optimization of hull shape (source: ©Sirehna/Naval Group). Fora col...Figure 2.43. Comparison of hull performance for different ship speeds (source: S...Figure 2.44. The Millau Viaduct, designed by the English architect Norman Foster...Figure 2.45. The simulation of the swimming of a fish uses an arbitrary Lagrangi...Figure 2.46. Movement of a fluid in a cryogenic reservoir [KON 19]. For a color ...Figure 2.47. Simulation of the impact of an object on a fluid surface [LER 04]. ...Figure 2.48. Algorithm applicable to the simulation of a deformable propeller. F...

3 Chapter 3Figure 3.1. Blaise Pascal (1623–1662)Figure 3.2. ALMA is an international astronomical observation tool, a network of...Figure 3.3. A summarizing history of the Universe. For a color version of this f...Figure 3.4. Simulation of the state of the Universe organized under gravitationa...Figure 3.5. Interactions between particles can be described with a network or tr...Figure 3.6. The Universe model proposed by Kepler is based on five regular polyh...Figure 3.7. Hypatia is played by Rachel Weisz in the film Agora [AME 09]Figure 3.8. Geoid: representation of the equipotentials of the gravitational fie...Figure 3.9. Lagrange points for the Sun and Earth. For a color version of this f...Figure 3.10. The Interplanetary Transport Network (ITN) passes through the Lagra...Figure 3.11. Signals sent between the Earth and the Cassini probe (green wave) a...Figure 3.12. Simulation of gravitational waves resulting from the interaction be...Figure 3.13. Aerial view of the LIGO interferometer in the United States (Living...Figure 3.14. First detection of gravitational waves, named after the day of thei...Figure 3.15. Examples of simulation in astrophysicsFigure 3.16. Highlighting the properties of certain numerical schemes [CHH 08]Figure 3.17. Stellar density map of our galaxy. For a color version of this figu...Figure 3.18. Stellar density calculations in a star cloud [LEE 17a]. For a color...Figure 3.19. Stellar density calculations [LEE 17b]. For a color version of this...Figure 3.20. Aquaplaning simulation [HEM 17]. For a color version of this figure...Figure 3.21. Illustration of Journey to the Center of the Earth [VER 64], plate ...Figure 3.22. Age of the oceanic lithosphere [MUL 11]. For a color version of thi...Figure 3.23. Recent seismic history of Italy (source: Emanuele Casarotti, Nation...Figure 3.24. Scenario for the L’Aquila earthquake aftershock: in yellow and red,...Figure 3.25. Traces of the earthquake on buildings in L’Aquila (source: ©Alain B...Figure 3.26. An underwater earthquake can cause a tsunami (source: © www.shuters...Figure 3.27. Estimated time for tsunami wave velocity induced by the Sendai eart...Figure 3.28. Tsunami wave height induced by the Sendai earthquake in 2011 estima...Figure 3.29. The Cumbre Vieja volcano in the Canary Islands last erupted in 1971...Figure 3.30. Experimental study of the flow of debris encountering a bumpFigure 3.31. Simulation of an avalanche of volcanic debris [KEL 05]. For a color...Figure 3.32. Red Fuji, Katsukicha Hokusaï (1760–1849), second view of the 36 Vie...Figure 3.33. Eruption of the Merapi volcano in 1930Figure 3.34. Simulation of the 2010 eruption of the Merapi volcano in Indonesia ...

4 Chapter 4Figure 4.1. Super Typhoon Maysak photographed by Italian engineer and pilot Sama...Figure 4.2. Emissions of substances into the Earth’s atmosphere (source: © NASA/...Figure 4.3. CO2 emissions from different sources (source: Our World in Data/http...Figure 4.4. Evolution of the average temperature at the Earth’s surface from 185...Figure 4.5. Meshing of the atmosphere (source: © ISPL/CEA-DSM). For a color vers...Figure 4.6. Numerical simulation of a cyclone off the island of Madagascar (sour...Figure 4.7. Simulation of wind conditions around: the wind scale is indicated in...Figure 4.8. Downscaling principle: local simulation on the Marseille region base...Figure 4.9. The main currents of the North Atlantic (source: © IFREMER). For a c...Figure 4.10. Offshore measurement system (source: © P. Lherminier/IFREMER)Figure 4.11. The international program “Argo” collects oceanological data throug...Figure 4.12. Evolution of ocean transport relative to the North Atlantic “convey...Figure 4.13. The Earth’s magnetic field measured from space (source: © ESA/www.e...Figure 4.14. Images of the magnetic field generated by ocean currents (source: h...Figure 4.15. The future of plastics production in 2015 (source: Our World in Dat...Figure 4.16. Estimated number and mass of plastic microparticles in the oceans [...Figure 4.17. “From mass production to mass production”: 3D printing to recycle a...Figure 4.18. The complexity of climate prediction models has increased in recent...Figure 4.19. The geographical resolution of successive generations of climate mo...Figure 4.20. Calculation of ocean surface temperature. For a color version of th...Figure 4.21. Contributing to the study of climate, numerical modeling is used to...Figure 4.22. Atmospheric simulations with cloud modeling (source: Kyle Pressel, ...Figure 4.23. Possible evolution of the Earth’s temperature under different green...Figure 4.24. Blue Marble: Earth photographed from space during the Apollo 17 mis...

5 Chapter 5Figure 5.1. The Salamanca (1812) – schema first published in The Mechanic’s Maga...Figure 5.2. Evolution of world energy consumption between 1965 and 2016 (source:...Figure 5.3. Back body calculation for Ariane V (source: ©ONERA). Fora color vers...Figure 5.4. Smoke and steam rising above an industrial complex (source: www.123r...Figure 5.5. Simulation of a gas turbine ignition sequence [BOI 08]. For a color ...Figure 5.6. X-ray of the bones of a hand with a ring on one finger, Wilhelm Konr...Figure 5.7. Nuclear energy is obtained by fission or fusion: if the former is a ...Figure 5.8. Nuclear fission (source: www.shutterstock.com). For a color version ...Figure 5.9. Schematic diagram of the operation of a nuclear power plant (source:...Figure 5.10. Power map of a pressurized water reactor [CAL 11]. For a color vers...Figure 5.11. Multiscale thermo-hydraulic calculations of a 4th generation reacto...Figure 5.12. Calculation of the LES in an reactor mixing grid (source: Christoph...Figure 5.13. The energy of the Sun and stars comes from the fusion of hydrogen (...Figure 5.14. Obtaining a plasma in a device: example of the European JET “tokama...Figure 5.15. Simulation of turbulence developing in a tokamak. For a color versi...Figure 5.16. Global investment in renewable energy (source: Our World in Data/ht...Figure 5.17. The Three Gorges Dam (source: www123rf.com)Figure 5.18. Francis turbine (1956), at the leading edges of cavitation-eroded b...Figure 5.19. Mesh size used for LES simulation of a turbine body [DOU 18]. For a...Figure 5.20. Offshore wind turbine fields (source: www123rf.com/Wang Song)Figure 5.21. Flow calculation around a vertical axis wind turbine (source: Insti...Figure 5.22. Wind measurement mast on a wind site (source: Le Télégramme/https:/...Figure 5.23. Evaluation of a site’s wind resource (source: calculation carried o...Figure 5.24. Evaluation of the effects of sunlight on an urban area using dynami...

6 Chapter 6Figure 6.1. Excerpt from Jean-Baptiste Sénac’s book, Traité de la structure du c...Figure 6.2. “In silico” model and new generation “in vitro” model. For a color v...Figure 6.3. The area to be operated on, in this case a tumor, is identified on a...Figure 6.4. Assisted robotic surgery (source: Jean-Marc Baste, CHU de Rouen)Figure 6.5. Cardiac ultrasound (source: www.shutterstock.com)Figure 6.6. Cardiac MRI (source: www.123.rf.com/Weerapong Tanawong-udom)Figure 6.7. Identification of the main fiber bundles of the brain based on diffu...Figure 6.8. Electrodes placed on a skull to perform an EEG (source: www.123rf.co...Figure 6.9. Implementation of the MEG at the CEA NeuroSpin Centre (source: © P. ...Figure 6.10. Sequencing techniques allow scientists to decode the human genome f...Figure 6.11. Finite element model of a leg’s soft tissue (source: image owned by...Figure 6.12. Pressure calculated in a foot under pressure on the ground (source:...Figure 6.13. Excerpt from William Harvey’s book, Exercitatio anatomica de motu c...Figure 6.14. Flow of a microcapsule (100 large microns) into a channel of the sa...Figure 6.15. Numerical simulation of ellipsoidal microcapsules in a single shear...Figure 6.16. Principle of angioplasty (source: www.123rf.com/Roberto Biasini)Figure 6.17. Experiments on a silicone model allow to validate the simulations [...Figure 6.18. Numerical simulation of blood flow in an arteriovenous fistula [DEC...Figure 6.19. Calculation model and simulation of an MRI [FOR 18]Figure 6.20. Simulation of stent placement in angioplasty: personalized arterial...Figure 6.21. Coupled fluid/structure simulations in the heart: blood flow rate i...Figure 6.22. Simulations of blood flow in a right (left) and curved (right) arte...Figure 6.23. Simulation of the electrical activity of a portion of a virtual bra...Figure 6.24. Galway neuro-morphic processor (source: Timothée Lévi, Université d...Figure 6.25. Interfering brains and machines: a dream or a nightmare within the ...

7 Chapter 7Figure 7.1. Bières de la Meuse, Alphonse Mucha, advertising poster, 1897, Biblio...Figure 7.2. John Nash (1928–2015)Figure 7.3. First measure of music of In My Life (represented as a tablature for...Figure 7.4. The Next Rembrandt, a table designed with digital techniques (source...Figure 7.5. An automatic analysis of personality traits. For a color version of ...Figure 7.6. Hierarchy of keywords #Sex (blue), #Weather (red), #Love (yellow), #...Figure 7.7. Which word is statistically more likely to complete a Google search ...Figure 7.8. Subjective map of the city of Nantes (source: http://www.geographies...Figure 7.9. Mobility simulation in the defense district. For a color version of ...Figure 7.10. Road noise map of the city of Nantes (source: IFSTTAR/CEREMA). For ...Figure 7.11. Acoustic propagation simulations with “detailed modeling”. For a co...Figure 7.12. The electrostatic force is attractive or repellent depending on the...Figure 7.13. The best places to open a bakery in Lyon (source: Pablo Jensen, Éco...Figure 7.14. A swarm of bees (source: www.shutterstock)Figure 7.15. A historical example of the rapid spread of unverified information ...Figure 7.16. Analysis of information relayed on Twitter during the French presid...Figure 7.17. Example of automatically generated text [RAD 19]Figure 7.18. The different forms of fear (source: www.atlasofemotions.org)Figure 7.19. Examples of Action Units (AU) from the Facial Action Coding System ...Figure 7.20. Observing and reproducing facial expressionsFigure 7.21. Vaugnet Rollins, Jeanloup Sieff, 1977 (source: © Jeanloup Sieff)

8 ConclusionFigure C.1. François Rabelais (1494–1553), anonymous, 16th Century, oil on canva...

9 Glossary of TermsFigure G.1. For its member countries, ESA is a gateway to spaceFigure G.2. Several decades of in situ experiments at INRAFigure G.3. The technical and scientific contributions of Mary Jackson, Katherin...Figure G.4. NASA’s robot on the ground on MarsFigure G.5. An algorithm in our daily lives: choosing your metro route (source: ...Figure G.6. AI nowadays corresponds to a set of concepts and techniques rather t...Figure G.7. Relationships between data of different kinds represented in the gra...Figure G.8. Blockchain operating principle (source: www.123rd.com)Figure G.9. Visualization of strange attractors (source: http://www.chaoscope.or...Figure G.10. Stress calculation in a mechanical part with the finite element met...Figure G.11. Global R&D investment in 2018 (source: How Much?, https://howmuch.n...

Numerical Simulation, An Art of Prediction, Volume 2

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