Numerical Simulation, An Art of Prediction 1

Theory

Jean-François Sigrist

• Publisher: Wiley-ISTE
• Year: 2019
• ISBN:
  9781119686712
• Edition: 1
• Topic: Matemáticas
• Subtopic: Análisis matemático

Numerical simulation is a technique of major importance in various technical and scientific fields. Used to understand diverse physical phenomena or to design everyday objects, it plays a major role in innovation in the industrial sector. Whilst engineering curricula now include training courses dedicated to it, numerical simulation is still not well-known in some economic sectors, and even less so among the general public. Simulation involves the mathematical modeling of the real world, coupled with the computing power offered by modern technology. Designed to perform virtual experiments, digital simulation can be considered as an "art of prediction". Embellished with a rich iconography and based on the testimony of researchers and engineers, this book shines a light on this little-known art. It is the first of two volumes and focuses on the principles, methods and industrial practice of numerical modeling.

1
The World in Equations

Written in the second half of the 19th Century, the novels by French writer Jules Verne (1828–1905) recall the scientific and technological progress of his century. Verne shared the positive conception of technological progress, theorized by the French philosopher Auguste Comte (1798–1857) among others. Confident in human inventiveness, he expressed it in these terms to the French explorer Charles Lemire (1839–1912), his first biographer: “Everything I imagine will always remain below the truth, because there will come a time when the creations of science will exceed those of imagination.”

Published in 1870, Twenty Thousand Leagues Under the Sea is one of his most translated works [VER 92]. Nowadays, it is also one of the top 20 best-selling books in the world, and has given rise to numerous adaptations for cinema, television and comic strips. Professor Aronnax, a leading expert at the Paris Museum of Natural History, Conseil, his servant, and Ned Land, an experienced sailor and harpooner, board the Abraham Lincoln, in search of a sea monster. The extraordinary beast is actually a machine of steel and electricity: the Nautilus, a formidable machine designed, built and commanded by Captain Nemo in order to rule the underwater world like a master. During their long stay aboard the submersible, the three heroes of the novel will discover magnificent landscapes and experience incredible adventures. They will measure the vastness of the ocean, its resources and wealth. A dream journey for Professor Aronnax, a golden prison for Ned Land, this strange epic will take them more than twenty thousand leagues under the sea. Verne lends these words to Captain Nemo:

If danger threatens one of your vessels on the ocean, the first impression is the feeling of an abyss above and below. On the Nautilus men’s hearts never fail them. No defects to be afraid of, for the double shell is as firm as iron; no rigging to attend to; no sails for the wind to carry away; no boilers to burst; no fire to fear, for the vessel is made of iron, not of wood; no coal to run short, for electricity is the only mechanical agent; no collision to fear, for it alone swims in deep water; no tempest to brave, for when it dives below the water it reaches absolute tranquility. There, sir! That is the perfection of vessels! And if it is true that the engineer has more confidence in the vessel than the builder, and the builder than the captain himself, you understand the trust I repose in my Nautilus; for I am at once captain, builder, and engineer! [VER 92]

How to make Captain Nemo’s dream come true? How to design a ship and ensure that its crew will be able to navigate safely, in difficult sea conditions or during sensitive operations? The engineers of the 21st Century have at their disposal the experience and know-how of those who preceded them, their physical sense and the sum of their technical knowledge – as well as the feedback of tragic accidents, some of which were told, for example, in the cinema [BIG 02, CAM 97]. Other tools are also available to them: those of numerical simulation* in particular [BES 06].

Figure 1.1. Numerical simulation nowadays accompanies the design of a ship as complex as a submarine [BOV 16, REN 15]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation1.zip

1.1 Numerical modeling

1.1.1 Modeling

Numerical simulation is based on the premise that it is possible to report physical phenomena – or others (biological, economic, demographic, physiological, etc.) – using mathematical models. Consisting of a set of equations, they are constructed with a number of assumptions limiting their use. The validity of the model is attested by a confrontation with physical reality and its precision in a given field is the subject of consent in the engineering community. Under these conditions, the mathematical model acquires an important predictive capacity. It can then be used to characterize the entity under study: for example, predict the lifecycle of an electrical device, the acoustic and thermal comfort of a performance venue, the fuel consumption of a car, the efficiency of a wind turbine, or the navigation speed of a submarine.

Since the time of Jules Verne, we have lived in a world in which techniques, the fruit of knowledge and practices transmitted by women and men, are present in the smallest objects of our daily lives. Nowadays, numerical simulation accompanies the entire life cycle of many industrial projects and productions, as the following simple example shows. In order to be comfortable to wear, a pair of glasses ought to be forgotten! Lenses and frames are often fragile, and by identifying their areas of fragility, the simulation makes it possible to choose lightweight materials and resistant shapes (Figure 1.2).

Figure 1.2. Strength calculation of a pair of glasses (Source: image made 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/simulation1.zip

COMMENT ON FIGURE 1.2.– The purpose of the calculation presented here is to identify the areas of fragility of a pair of glasses. It is based on equations describing the mechanical behavior of materials (lenses, frames) and produces data that can be used by engineers. These are represented on the object using a color code: the red areas indicate potential breakpoints. The calculation is in line with our experience: in most cases, the frame will tend to break through the thin junction zone between the two lenses…

Numerical simulation is nowadays a must in the industrial world and in many scientific disciplines. It contributes significantly to innovation in this sector, by meeting two main objectives:

• – the control of technical risks. It allows the creation of regulatory dossiers, the demonstration of safety and reliability, the preparation of environmental impact studies, etc.;
• – economic performance. It contributes to the optimization of products, the demonstration of their robustness, the prediction of their performance or the reduction of their manufacturing and operating costs [COZ 09].

From their design to their dismantling, including their production, commissioning and operation, simulation becomes a general tool that benefits from the development of digital techniques. Nowadays, computer calculation makes it possible to model* many physical phenomena with satisfa...

Table of contents

• Cover
• Table of Contents
• Foreword
• Preface
• Acknowledgements
• 1 The World in Equations
• 2 Simulation Practice
• 3 A Global Technique
• 4 The Data World
• Conclusion
• Glossary of Terms
• References
• Index
• End User License Agreement