A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws
Badsi, Mehdi1 ; Berthon, Christophe1 ; Martaud, Ludovic1
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, Tome 9 (2023), pp. 31-60
corrigé par 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.

Publié le :
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.

Badsi, Mehdi 1 ; Berthon, Christophe 1 ; Martaud, Ludovic 1

1 Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France 
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Badsi, Mehdi; Berthon, Christophe; Martaud, Ludovic. A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws. The SMAI Journal of computational mathematics, Tome 9 (2023), pp. 31-60. doi: 10.5802/smai-jcm.94

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