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 several families of physically relevant steady states. In this paper we design a well-balanced numerical scheme for the one-dimensional shallow water magnetohydrodynamic system with topography, that resolves exactly a large range of steady states. Two variants are proposed with slightly different families of preserved steady states. They are obtained by a generalized hydrostatic reconstruction algorithm involving the magnetic field and with a cutoff parameter to remove singularities. The solver is positive in height and semi-discrete entropy satisfying, which ensures the robustness of the method.

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. Numerische Mathematik, 2017, 136 (4), pp.875-905. ⟨10.1007/s00211-017-0865-y⟩. ⟨hal-01131297v3⟩