Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For continuous entropy analysis to hold and ensure Galilean invariance in technique, system requires use of non-conservative terms. Traditionally, DG discretizations have used collocated nodal variant method, also known as spectral element (DGSEM) Legendre-Gauss-Lobatto (LGL) points. Recently, Chan et al. [1, “Efficient Entropy Stable Collocation Methods”. SIAM (2019)] presented DGSEM scheme that uses Legendre-Gauss points (instead LGL points) conservation laws. Our main contribution is extend discretization technique system. We provide numerical verification behavior convergence properties our novel meshes. Moreover, test robustness accuracy magneto-hydrodynamic Kelvin-Helmholtz instability problem. The experiments suggest more accurate than counterpart.