Geodesic
A novel second order accurate hybrid numerical approach for conservation laws
Pascal Jaisson1, 2 ; 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
ESAIM. Proceedings, Tome 25 (2008), pp. 91-113.

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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.
DOI : 10.1051/proc:082507

Pascal Jaisson 1, 2 ; Florian De Vuyst 2, 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 
@article{EP_2008_25_a7,
     author = {Pascal Jaisson and Florian De Vuyst},
     title = {A novel second order accurate hybrid numerical approach for conservation laws},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc:082507},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:082507/}
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Pascal Jaisson; Florian De Vuyst. A novel second order accurate hybrid numerical approach for conservation laws. ESAIM. Proceedings, Tome 25 (2008), pp. 91-113. doi : 10.1051/proc:082507. http://geodesic.mathdoc.fr/articles/10.1051/proc:082507/

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