A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws

Mehdi Badsi (1) , Christophe Berthon (1) , Ludovic Martaud (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Systems of conservation laws; Second-order finite Volume schemes; Explicit schemes; Global entropy inequality. Math. classification. 65N08

Domaines: Analyse numérique [math.NA]; Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Mehdi Badsi, Christophe Berthon, Ludovic Martaud. A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws. 2022. ⟨hal-03564325v1⟩