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.

在本文中，我们基于适当的正交规则，为十矩高斯封闭方程提出了高阶不连续Galerkin熵稳定方案（请参见[1]）。提出的方案的关键组成部分是在每个像元中使用熵保守数值通量[2]，并在像元边缘使用适当的熵稳定数值通量。然后将这些通量用于[1]的熵稳定DG框架中，以获得半离散方案的熵稳定性。我们还将这些方案扩展到模拟等离子体激光相互作用的源术语。对于时间离散，我们使用强稳定性保持方法。然后在几个测试用例上测试提出的方案，以证明其稳定性，准确性和鲁棒性。