Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes

We present a finite volume scheme for ideal compressible magnetohydrodynamic (MHD) equations on two-dimensional Cartesian meshes. The semidiscrete scheme is constructed to be entropy stable by using the symmetrized version of the equations as introduced by Godunov. We first construct an entropy conservative scheme for which sufficient condition is given and we also derive a numerical flux satisfying this condition. Second, following a standard procedure, we make the scheme entropy stable by adding dissipative flux terms using jumps in entropy variables. A semi-discrete high resolution scheme is constructed that preserves the entropy stability of the first order scheme. We demonstrate the robustness of this new scheme on several standard MHD test cases.

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