Kröger, TimTimKrögerMedviďová-Lukáčová, MáriaMáriaMedviďová-Lukáčová2006-02-142006-02-142004-04Preprint. Published in: Journal of Computational PhysicsVolume 206, Issue 1, 10 June 2005, Pages 122-149http://tubdok.tub.tuhh.de/handle/11420/122In 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.enhttp://rightsstatements.org/vocab/InC/1.0/genuinely multidimensional schemeshyperbolic systemsshallow water magnetohydrodynamic equationfinite volume methodsMathematikPreprint2006-02-17urn:nbn:de:gbv:830-opus-178710.15480/882.120EvolutionsoperatorGalerkin-MethodeErhaltungssatzMagnetohydrodynamische GleichungInitial value problems for hyperbolic systems of first-order PDEShocks and singularitiesMethod of characteristicsMagnetohydrodynamics and electrohydrodynamicsConservation lawsFinite difference methods11420/12210.1016/j.jcp.2004.11.03110.15480/882.120930767999Other