Entropy stable scheme for ideal MHD equations on adaptive unstructured meshes

Abstract

An entropy stable scheme based on adaptive unstructured meshes for solving ideal magnetohydrodynamic (MHD) equations is proposed. Firstly, a semi-discrete finite volume scheme is constructed on unstructured meshes, which includes entropy conservative flux and Roe-type dissipation operator. Particularly, a special discrete Godunov source term is added to control magnetic field divergence, and it is proved that the new scheme is entropy stable. Secondly, the accuracy of the basic entropy stable scheme is enhanced through reconstruction of the entropy dissipation operator using the minmod slope limiter. Finally, based on the adaptive moving meshes, a new monitor function is designed for the properties of the ideal MHD equation solution, which can effectively identify the large gradient areas of the solution and optimize the mesh distribution. Several numerical examples illustrate that the novel scheme exhibits high accuracy and proficiently captures shock waves.