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Issue ESAIM: Proc.
Volume 25, 2008
Paris-sud working group on modelling and scientific computing 2007-2008
Page(s) 91 - 113
DOI http://dx.doi.org/10.1051/proc:082507
Published online 16 January 2009

ESAIM: Proc., 2008, Vol. 25, pp. 91-113
DOI: 10.1051/proc:082507

A novel second order accurate hybrid numerical approach for conservation laws

Pascal Jaisson1, 2 and Florian De Vuyst2, 3, 4

1  CMAP, Ecole Polytechnique, INRIA Saclay-Ile-de-France, Equipe COMMANDS, Route de Saclay, 91128 Palaiseau cedex, FRANCE
2  Laboratoire MAS, Ecole Centrale Paris, Grande voie des vignes 92295 Châtenay-Malabry cedex FRANCE
3  CMLA, ENS Cachan, 94235 Cachan cedex, FRANCE
4  Energy Conversion Research Center, Doshisha University, Kyotanabe campus, Kyoto, Japan


Published online: 16 January 2009

Abstract
In this paper, we present a novel one-parameter hybrid scheme for hyperbolic systems of conservation laws. The parameter value can be adapted in each numerical cell in order to obtain the advantages of Lax-Wendroff flux (second order scheme) where the solution is locally smooth. On the other hand, the scheme can switch to the Lax-Friedrichs one if necessary in order to be oscillation free (Total Variation Diminushing). Various numerical examples illustrate the efficiency of our scheme.


Résumé
Nous proposons dans cet article un nouveau schéma hybride à un paramètre pour les systèmes hyperboliques de lois de conservation. Le paramètre permet d'obtenir les bonnes propriétés du schéma de Lax-Wendroff lorsque la solution est régulière (schéma du second ordre) et de respecter la propriété de "Total Variation Diminushing" dans chaque cellule en utilisant si nécessaire le flux de Lax-Friedrichs. Nous présentons quelques expériences numériques illustrant l'efficacité de la méthode.



© EDP Sciences, ESAIM 2008


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