Course Syllabus 2015/2016
 
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Module : AN200
Title :
Numerical approximation and industrial problems I
Number of hours :
Lecture : 18.00 h
Tutorial classes : 25.33 h
Individual work : 22.00 h
ECTS credits :
4.00
Evaluation :
Teacher(s) :
AREGBA Denise - Responsible
BRULL Stéphane
Shared by UV(s) :
Level :
second year module
Abstract :
The goal of this course is to show some fundamental elements of numerical approximation of partial differential equations. Linear evolution equations involving transport and diffusion phenomenons which can be observed in most of mechanical problems are discretized by two methods: finite differences and finite volumes.

Main notions like accuracy, stability, convergence, numerical diffusion and dispersion, are analyzed. Implementation is carefully studied. The numerical methods presented in the course are studied with exercices and programming sessions.

Plan :
    • PDEs in Mechanics
    • Finite difference method in 1D.
    • Finite volume method in 1D.
    • Finite volume method in 2D: cartesian meshes, unstructured meshes.
    • Additionnal features on linear hyperbolic systems and high order finite volume methods.
Document(s) :
    • Polycopié de cours.
    • Lionel Sainsaulieu, Calcul scientifique. Cours et exercices corrigés pour le 2ème cycle et les écoles d'ingénieurs. Deuxième édition. - Dunod, 2000.
    • Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.