# Entropy stable finite volume scheme for ideal MHD

The equations of compressible MHD can only be symmetrized by adding terms containing the divergence of the magnetic field as shown by Godunov. In this work, we propose sufficient conditions on the numerical flux which leads to an entropy conservative scheme for the MHD equations. Using this condition we construct an explicit formula for the numerical flux. An entropy stable scheme is obtained by adding dissipative flux based on entropy variables. Higher order versions of the entropy stable scheme are constructed and tested for one and two dimensional problems. The schemes are able to compute discontinuous solutions in a stable manner.

**People**: Praveen C, Christian Klingenberg

**Status**: Completed, article in SINUM