In this article, we consider the Chew, Goldberger \& Low (CGL) plasma flow equations, which is a set of nonlinear, non-conservative hyperbolic PDEs modelling anisotropic plasma flows. These equations incorporate the double adiabatic approximation for the evolution of the pressure, making them very valuable for plasma physics, space physics and astrophysical applications. We first present the entropy analysis for the weak solutions. We then propose entropy-stable finite-difference schemes for the CGL equations. The key idea is to rewrite the CGL equations such that the non-conservative terms do not contribute to the entropy equations. The conservative part of the rewritten equations is very similar to the magnetohydrodynamics (MHD) equations. We then symmetrize the conservative part by following Godunov's symmetrization process for MHD. The resulting equations are then discretized by designing entropy conservative numerical flux and entropy diffusion operator based on the entropy scaled eigenvectors of the conservative part. We then prove the semi-discrete entropy stability of the schemes for CGL equations. The schemes are then tested using several test problems derived from the corresponding MHD test cases.

翻译：本文研究 Chew、Goldberger 与 Low (CGL) 等离子体流动方程组，这是一组用于模拟各向异性等离子体流动的非线性、非守恒双曲型偏微分方程。该方程组采用双绝热近似描述压力的演化，因此在等离子体物理、空间物理和天体物理应用中具有重要价值。我们首先给出了弱解的熵分析。随后，针对 CGL 方程提出了熵稳定的有限差分格式。其核心思想在于重构 CGL 方程，使得非守恒项对熵方程不产生贡献。重构方程的守恒部分与磁流体动力学 (MHD) 方程高度相似。我们继而遵循 Godunov 的 MHD 对称化方法，对该守恒部分进行对称化处理。基于守恒部分的熵尺度特征向量，通过设计熵守恒数值通量和熵扩散算子，对所得方程进行离散化。我们随后证明了该格式对 CGL 方程的半离散熵稳定性。最后，利用从相应 MHD 测试案例推导出的若干算例，对所提格式进行了数值验证。