Geodesic
Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes
Mohammed Boujoudar1 ; Emmanuel Franck2 ; Philippe Hoch3 ; Clément Lasuen3 ; Yoan Le Hénaff4 ; Paul Paragot5
1 Mohammed VI Polytechnic University, Morocco
2 Université de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France
3 CEA, DAM, DIF, 91297, Arpajon Cedex, France
4 Université de Rennes, IRMAR UMR 6625, Centre INRIA de l’Université de Rennes (MINGuS), France
5 Laboratoire J.A. Dieudonné, Université Côte d’Azur, France
ESAIM. Proceedings, Tome 77 (2024), pp. 123-144.

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In this work we focus on an adaptation of the method described in [1] in order to deal with source term in the 2D Euler equations. This method extends classical 1D solvers (such as VFFC, Roe, Rusanov) to the two-dimensional case on unstructured meshes. The resulting schemes are said to be composite as they can be written as a convex combination of a purely node-based scheme and a purely edge-based scheme. We combine this extension with the ideas developed by Alouges, Ghidaglia and Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at discretizing the source term of the Euler equations in order to better preserve stationary solutions. We compare these discretizations with the “usual” centered discretization on several numerical examples.
DOI : 10.1051/proc/202477123

Mohammed Boujoudar 1 ; Emmanuel Franck 2 ; Philippe Hoch 3 ; Clément Lasuen 3 ; Yoan Le Hénaff 4 ; Paul Paragot 5

1 Mohammed VI Polytechnic University, Morocco
2 Université de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France
3 CEA, DAM, DIF, 91297, Arpajon Cedex, France
4 Université de Rennes, IRMAR UMR 6625, Centre INRIA de l’Université de Rennes (MINGuS), France
5 Laboratoire J.A. Dieudonné, Université Côte d’Azur, France 
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     author = {Mohammed Boujoudar and Emmanuel Franck and Philippe Hoch and Cl\'ement Lasuen and Yoan Le H\'enaff and Paul Paragot},
     title = {Cemracs project: {A} composite finite volume scheme for the {Euler} equations with source term on unstructured meshes},
     journal = {ESAIM. Proceedings},
     pages = {123--144},
     publisher = {mathdoc},
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     year = {2024},
     doi = {10.1051/proc/202477123},
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     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477123/}
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Mohammed Boujoudar; Emmanuel Franck; Philippe Hoch; Clément Lasuen; Yoan Le Hénaff; Paul Paragot. Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes. ESAIM. Proceedings, Tome 77 (2024), pp. 123-144. doi : 10.1051/proc/202477123. https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477123/

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