TB3 - ADVANCED MODELING AND NUMERICAL SIMULATION

In the practice of his profession, an engineer will often find himself confronted by problems involving complex physical phenomena. In such a context recourse to modelling (analytical or digital) appears obvious, but the growing complexity of models will often lead the engineer towards numerically obtained approximate solutions (typically the Finite Element method (FE).

Today, numerical simulation is used in numerous industrial fields in research and development: solid mechanics, fluid mechanics, materials science, astrophysics, nuclear physics, aeronautics, climatology, meteorology, theoretical physics, quantum mechanics, biology, chemistry ..

Numerical simulation refers to the process whereby programmes are run on a computer with a view to representing a physical phenomenon. Scientific numerical simulations rely on the application of theoretical models. They are therefore an adaptation of mathematical models to numerical means. They serve to study the functioning of system properties and to predict their evolution.

The construction of a physical model (using mathematical equations), followed by the elaboration of a numerical strategy, thus represent the central task for an engineer confronted by a scientific problem. Future engineers can therefore acquire:

• The scientific perspective necessary for the analysis/interpretation of results through knowledge of equations
• The know-how for implementing a modelling approach
• The knowledge of problem solving methods, numerical patterns and the structure of calculation codes.

The “Advanced numerical modelling and simulation” Toolbox is divided into 4 units of approx. 20 h each.

Following on from the 1st year teaching of physics, mathematics, mechanical engineering, and computer science, the first unit will enable students to understand the mathematical concepts linked to a modelling approach, from the main fundamentals through to the analysis of Partial Differential Equations (PDE), including the notion of approximation. The second unit enables students to acquire knowledge of the methods/techniques for solving PDE established in the first unit, from discretisation by the Finite Element method through to systems solutions. The third unit will provide further knowledge of the notion of convergence of solutions linked to behavioural problems of non-linear materials, and of instabilities or complex boundary conditions (contact), in particular for applications of solid mechanics and structures. The last unit enables the student to deal with specific concepts linked to transfer phenomena and mobile interfaces, from the writing of mixed formulations necessary for the processing of incompressibility through to their stabilisation.

• Introduction to mathematical concepts necessary for numerical modelling and simulation - Unit 1 The Finite Element method
• Methods and techniques for solving PDE – Unit 2 Mathematical analysis and numerical discretisation
• Processing problems of solid mechanics and of structures – Unit 3 Non-linear problems in mechanics
• Modelling and simulation of transfer phenomena – Unit 4 Transfer Phenomena

The transversal nature of the Advanced numerical modelling and simulation Toolbox opens up several possibilities of interactions with other Majors, Interdisciplinary specialisations and Toolboxes.

It presents a solid base for dealing with numerical modelling and simulation in the Mechanical Engineering, Materials Science or Process Engineering majors.

Without being exhaustive, the knowledge acquired in this Advanced numerical modelling and simulation Toolbox could be completed by skills in:

·         Design (CAD Virtualisation/Materialisation Toolbox, Ecodesign specialisation)

·         Scientific calculation (Tensor calculus toolbox)

·         Intensive calculating (High Performance Computing Toolbox)