Digital simulation

Through a lecture followed by hands-on experience with typical CFD (Computational Fluid Dynamics) software, this course provides an introduction to the modeling approach (formulation of a problem, choice of hypotheses) and its corollary, simulation (resolution of the problem posed using appropriate tools). The objectives of these few hours of training are:

to know how to formulate a problem with a view to its simulation (in relation to physical models)
to understand the structure of a numerical code and the sequence of operations,
to understand the role of the numerical methods used (in relation to numerical analysis courses)
to become aware of some of the "pitfalls" of simulation,
to know how to produce numerical results, criticize them (in relation to theoretical knowledge), and present them, including graphically
to appreciate the contribution, but also the limits, of numerical simulation.

Basic knowledge of Heat and Mass Transfer and Fluid Mechanics
Elements of Numerical Analysis (solving linear systems, minimization)
Handling of standard office tools (WINDOWS, EXCEL)

General

Introduction: objectives, procedure
What is a numerical code? construction stages, skills required
Generic form of conservation equations, terminology, Velocity-Pressure coupling
Boundary conditions and initial conditions

Spatial discretization and associated resolution techniques

The different types of mesh (structured, unstructured, adaptive)
The Finite Difference method: illustration on a 1D parabolic equation (explicit-implicit treatment)
"Philosophy" and Practical application of the Finite Volume technique: example on the Energy Equation Philosophy" and practical application of the Finite Volume technique: example on the Energy Equation

Analysis of some results

Some precautions before getting started ... or illustrations of pitfalls: solving a non-linear energy equation, tracking an unsteady phenomenon with an unsuitable time step, bifurcation of solutions, etc.
Conclusions

Practical application

Learning on 2 basic cases (flow in a pipe, natural thermal convection in a cavity): getting to grips with the CFD software Fluent and the associated graphics software (visualization - processing of results)
Handling of an individualized case (conductivity of a composite, injection of a polymer, planar exchanger, etc.)

Physics

Résolution Numérique des Equations aux Dérivées Partielles, de la Physique de la Mécanique, et des Sciences de l'Ingénieur, D. Euvrard (2ème Edition), MASSON Editeurs, 1990
Numerical Recipes, The Art of Scientific Computing, CAMBRIDGE UNIVERSITY PRESS, 1990
Numerical Heat Transfer and Fluid Flow, S. Patankar, TAYLOR and FRANCIS Ed, 1980
Computational Methods for Fluid Dynamics, J. H. Ferziger, M. Peric, SPRINGER Verlag, 1996 (reissued 1999)
Traité des Matériaux, Vol. 10 : Modélisation Numérique en Science et Génie des Matériaux, M. Rappaz, M. Bellet, M. Deville, Presses Polytechniques et Universitaires Romandes, 1998