A composite finite volume scheme for the Euler equations with source term on unstructured meshes
Résumé
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Tajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts at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
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