A multi well-balanced scheme for the shallow water MHD system with topography

François Bouchut (1) , Xavier Lhébrard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The shallow water magnetohydrodynamic system involves different families of physically relevant steady states. In this paper, we design a well-balanced numerical scheme for the shallow water magnetohydro-dynamic system with topography, that resolves exactly a large family of steady states. It is obtained by a generalized hydrostatic reconstruction algorithm involving the magnetic field. It is positive in height and semi-discrete entropy satisfying, which ensures the robustness of the scheme.

Mots clés: Shallow water magnetohydrodynamics; topography; well-balanced scheme; hydrostatic reconstruction; semi-discrete entropy inequality

Domaines: Analyse numérique [math.NA]

François Bouchut, Xavier Lhébrard. A multi well-balanced scheme for the shallow water MHD system with topography. 2015. ⟨hal-01131297v1⟩