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Issue ESAIM: Proc.
Volume 22, 2008
CANUM 2006 - Congrès National d'Analyse Numérique
Page(s) 52 - 66
DOI http://dx.doi.org/10.1051/proc:072205
Published online 01 February 2008

ESAIM: Proc., 2008, Vol. 22, pp. 52-66
DOI: 10.1051/proc:072205

AHO schemes for Dissipative Hyperbolic Systems

Denise Aregba-Driollet1, Maya Briani2 and Roberto Natalini2

1  Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux 1
2  Istituto per le Applicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche & Università LUISS - Guido Carli di Roma


(... / Published online: 1 February 2008)

Abstract
We study finite difference schemes which approximate $2\times 2$ linear one dimensional dissipative hyperbolic systems. We introduce suitable modifications of standard upwinding schemes to keep into account the long-time behaviour of the solutions, which consist in some schemes which are increasingly accurate for large times. This property of accuracy is required in order to get better results for large time simulations when computing perturbations of some given stable states, both in the steady state and in the diffusion limit.


Résumé
Nous présentons des schémas aux différences finies pour des systèmes hyperboliques linéaires dissipatifs $2\times 2$ en une dimension d'espace. Afin de tenir compte du comportement asymptotique de la solution, nous modifions des schémas "upwind" classiques pour construire des approximations dont la précision augmente avec le temps. Cette technique nous permet d'améliorer sensiblement les résultats des simulations en grands temps pour les perturbations des états asymptotiquement stables, tant autour des états stationnaires que dans la limite diffusive.


Mathematics Subject Classification. Primary: 65M12; Secondary: 35L65

Key words: finite differences methods, dissipative hyperbolic problems, asymptotic behavior, asymptotic high order schemes


© EDP Sciences, ESAIM 2007


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