35L45:Initial value problems for hyperbolic systems of first-order PDE
35L67:Shocks and singularities
65M25:Method of characteristics
76W05:Magnetohydrodynamics and electrohydrodynamics
35L65:Conservation laws
65M06:Finite difference methods
35L67
35L45
65M06
35L65
76W05
65M25
Beschreibung:
In this paper we propose a new finite volume evolution Galerkin(FVEG) scheme for the shallow water magnetohydrodynamic (SMHD)equations. We apply the exact evolution operator already used in our earlier publications to the SMHD system. Then, we approximate the evolution operator in a general way which does not exploit any particular property of the SMHD equations and should thus be applicable to arbitrary systems of hyperbolic conservation laws in two space dimensions. In particular, we investigate more deeply the approximation of the spatial derivatives which appear in the evolution operator. The divergence free condition is satisfied discretely, i.e. at each vertex. First numerical results confirm reliability of the numerical scheme.