A composite finite volume scheme for the Euler equations with source term on unstructured meshes

A composite finite volume scheme for the Euler equations with source term on unstructured meshes

In this work we focus on an adaptation of the method described in [1] in order to deal withsource 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 becomposite as...

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Bibliographic Details
Published in:ESAIM. Proceedings and surveys pp. 1 - 22
Main Authors: Boujoudar, Mohamed, Franck, Emmanuel, Hoch, Philippe, Lasuen, Clément, Le Henaff, Yoann, Paragot, Paul
Format: Journal Article
Language:English
Published: EDP Sciences 2024
Subjects:
Mathematics
Numerical Analysis
Finite Volume Method
Well Balanced Method
Composite Flux Schemes
Compressible Euler equations with sources
Online Access:Get full text
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Summary:In this work we focus on an adaptation of the method described in [1] in order to deal withsource 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 becomposite as they can be written as a convex combination of a purely node-based scheme and a purelyedge-based scheme. We combine this extension with the ideas developed by Alouges, Ghidaglia andTajchman in an unpublished work [2] – focused mainly on the 1D case – and we propose two attempts atdiscretizing the source term of the Euler equations in order to better preserve stationary solutions. Wecompare these discretizations with the “usual” centered discretization on several numerical examples
ISSN:2267-3059
2267-3059