Geodesic
Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number
Stéphane Dellacherie1 ; Jonathan Jung2 ; Pascal Omnes3
1 CEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Pierre et Marie Curie, LRC Manon and LJLL, 4 place Jussieu, 75252 Paris, cedex 05, France,
2 EFREI & AlliansTIC, 30-32 avenue de la République, 94800 Villejuif, France and Université Pierre et Marie Curie, LRC Manon and LJLL, 4 place Jussieu, 75252 Paris, cedex 05, France and LMA-IPRA, Université de Pau et des Pays de l’Adour, UMR CNRS 5142, Avenue de l’Université, 64013 Pau, France and INRIA Bordeaux Sud Ouest, Cagire Team, 351 Cours de la Libération, 33405 Talence, France,
3 CEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539, 99, Avenue J.-B. Clément F-93430 Villetaneuse Cedex, France,
ESAIM. Proceedings, Tome 52 (2015), pp. 105-126.

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We introduce continuous tools to study the low Mach number behavior of the Godunov scheme applied to the linear wave equation with porosity on cartesian meshes. More precisely, we extend the Hodge decomposition to a weighted L2 space in the continuous case and we study the properties of the modified equation associated to this Godunov scheme. This allows to partly explain the inaccuracy of the Godunov scheme at low Mach number on cartesian meshes and to propose two corrections: a first one named low Mach and a second one named all Mach. These results are preliminary since it remains to prove them in the discrete case.
DOI : 10.1051/proc/201552006

Stéphane Dellacherie 1 ; Jonathan Jung 2 ; Pascal Omnes 3

1 CEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Pierre et Marie Curie, LRC Manon and LJLL, 4 place Jussieu, 75252 Paris, cedex 05, France,
2 EFREI & AlliansTIC, 30-32 avenue de la République, 94800 Villejuif, France and Université Pierre et Marie Curie, LRC Manon and LJLL, 4 place Jussieu, 75252 Paris, cedex 05, France and LMA-IPRA, Université de Pau et des Pays de l’Adour, UMR CNRS 5142, Avenue de l’Université, 64013 Pau, France and INRIA Bordeaux Sud Ouest, Cagire Team, 351 Cours de la Libération, 33405 Talence, France,
3 CEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539, 99, Avenue J.-B. Clément F-93430 Villetaneuse Cedex, France, 
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     author = {St\'ephane Dellacherie and Jonathan Jung and Pascal Omnes},
     title = {Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number},
     journal = {ESAIM. Proceedings},
     pages = {105--126},
     publisher = {mathdoc},
     volume = {52},
     year = {2015},
     doi = {10.1051/proc/201552006},
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Stéphane Dellacherie; Jonathan Jung; Pascal Omnes. Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number. ESAIM. Proceedings, Tome 52 (2015), pp. 105-126. doi : 10.1051/proc/201552006. http://geodesic.mathdoc.fr/articles/10.1051/proc/201552006/

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