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

TL;DR

This paper develops high-order entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations, ensuring stability and robustness for plasma modeling applications.

Contribution

It introduces entropy stable DG schemes using entropy conservative fluxes and extends them to plasma laser interaction source terms.

Findings

Schemes demonstrate stability and accuracy in test cases

Method ensures entropy stability for complex plasma equations

Extended to include plasma laser interaction effects

Abstract

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.