In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use of an entropy conservative numerical flux [31] in each cell and a suitable entropy stable numerical flux at the cell edges. This is then used in the entropy stable DG framework of [8] to obtain entropy stability of the semi-discrete scheme. We also extend these schemes to a source term that models plasma laser interaction. For the time discretization, we use strong stability preserving schemes. The proposed schemes are then tested on several test cases to demonstrate stability, accuracy, and robustness.

中文翻译：

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十矩高斯闭合方程的熵稳定不连续伽辽金方法

在本文中，我们为十矩高斯闭合方程提出了高阶不连续伽辽金熵稳定方案，该方案基于合适的正交规则（参见 [8]）。所提出方法的关键组成部分是在每个单元中使用熵保守数值通量 [31] 以及在单元边缘使用合适的熵稳定数值通量。然后将其用于 [8] 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项。对于时间离散化，我们使用强稳定性保持方案。然后在几个测试用例上测试所提出的方案，以证明稳定性、准确性和鲁棒性。