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Issue ESAIM: PROC
Volume 15, 2005
GRIP - Research Group on Particle Interactions
Page(s) 1 - 17
DOI 10.1051/proc:2005020

ESAIM: Proc., 2005, Vol. 15, pp. 1-17
DOI: 10.1051/proc:2005020

An introduction to finite volume methods for hyperbolic conservation laws

Francois Bouchut

Département de Mathématiques et Applications, DMA - UMR 8553, Ecole Normale Supérieure 45, rue d'Ulm 75230 Paris cedex 05 - France.

Francois.Bouchut@ens.fr

Abstract
Hydrodynamic transport problems often take the form of systems of hyperbolic conservation laws. This minicourse intends to introduce the main notions and tools for the numerical approximation of such systems by finite volumes. The notions of consistency, stability, and approximate Riemann solvers are explained in particular. The main ingredients to go to second-order and multidimension are given.


Résumé
Les problèmes de transport hydrodynamique prennent souvent la forme de systèmes de lois de conservation hyperboliques. Ce cours vise à introduire les notions principales et les outils pour l'approximation numérique de tels systèmes par des volumes finis. En particulier, les notions de consistance, stabilité et solveurs de Riemann approchés sont expliquées. On donne aussi les arguments principaux pour passer au second ordre et aux cas multi-dimensionnels.


Key words: Systems of conservation laws - finite volumes - invariant domains - entropy inequalities - approximate Riemann solver


© EDP Sciences, ESAIM 2005


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