Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Abstract

In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, based on the suitable quadrature rules (see [1]). The key components of the proposed schemes are the use of an entropy conservative numerical flux [2] in each cell and an appropriate entropy stable numerical flux at the cell edges. These fluxes are then used in the entropy stable DG framework of [1] to obtain entropy stability of the semi-discrete schemes. We also extend these schemes to a source term that models plasma laser interaction. For the time discretization, we use strong stability preserving methods. The proposed schemes are then tested on several test cases to demonstrate stability, accuracy and robustness.