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.
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