Free access article

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

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

• If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
• You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
• You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.