Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2015-12-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201552006 |
| _version_ | 1828075797316894720 |
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| author | Dellacherie Stéphane Jung Jonathan Omnes Pascal |
| author_facet | Dellacherie Stéphane Jung Jonathan Omnes Pascal |
| author_sort | Dellacherie Stéphane |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T02:04:51Z |
| format | Article |
| id | doaj.art-231c66c52a4244138840b0e140757016 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:04:51Z |
| publishDate | 2015-12-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-231c66c52a4244138840b0e1407570162023-01-03T03:16:30ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592015-12-015210512610.1051/proc/201552006proc155206Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach numberDellacherie Stéphane0Jung Jonathan1Omnes Pascal2CEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Pierre et Marie Curie, LRC Manon and LJLLEFREI & 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 TeamCEA, DEN, DM2S, STMF F-91191, Gif-sur-Yvette, France and Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539We 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.http://dx.doi.org/10.1051/proc/201552006 |
| spellingShingle | Dellacherie Stéphane Jung Jonathan Omnes Pascal Preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number ESAIM: Proceedings and Surveys |
| title | Preliminary results for the study of the godunov scheme
applied to the linear wave equation with porosity
at low mach number |
| title_full | Preliminary results for the study of the godunov scheme
applied to the linear wave equation with porosity
at low mach number |
| title_fullStr | Preliminary results for the study of the godunov scheme
applied to the linear wave equation with porosity
at low mach number |
| title_full_unstemmed | Preliminary results for the study of the godunov scheme
applied to the linear wave equation with porosity
at low mach number |
| title_short | Preliminary results for the study of the godunov scheme
applied to the linear wave equation with porosity
at low mach number |
| title_sort | preliminary results for the study of the godunov scheme applied to the linear wave equation with porosity at low mach number |
| url | http://dx.doi.org/10.1051/proc/201552006 |
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