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A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws
Mehdi Badsi1; Christophe Berthon1; Ludovic Martaud1
1 Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 31-60.
corrected-by Erratum to : “A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws”

We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.

Published online:
DOI: 10.5802/smai-jcm.94
Classification: 65N08, 35L65, 35L67
Keywords: Systems of conservation laws, Second-order finite Volume schemes, Explicit schemes, Global entropy inequality.

Mehdi Badsi 1; Christophe Berthon 1; Ludovic Martaud 1

1 Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Mehdi Badsi; Christophe Berthon; Ludovic Martaud. A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws. The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 31-60. doi : 10.5802/smai-jcm.94. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.94/

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