| Issue |
ESAIM: ProcS
Volume 77, 2024
CEMRACS 2022 - Transport in physics, biology and urban traffic
|
|
|---|---|---|
| Page(s) | 123 - 144 | |
| DOI | https://doi.org/10.1051/proc/202477123 | |
| Published online | 18 November 2024 | |
Cemracs project: A composite finite volume scheme for the Euler equations with source term on unstructured meshes*
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
CEA, DAM, DIF, 91297, Arpajon Cedex, France
5
Université de Rennes, IRMAR UMR 6625, Centre INRIA de l’Université de Rennes (MINGuS), France
6
Laboratoire J.A. Dieudonné, Université Côte d’Azur, France
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 We combine this extension with the ideas developed by Alouges, Ghidaglia and Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at discretizing the source term of the Euler equations in order to better preserve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.
© EDP Sciences, SMAI 2024
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