Chew, Goldberger & Low各向异性等离子体流动方程的熵稳定有限差分格式
Entropy stable finite difference schemes for Chew, Goldberger & Low anisotropic plasma flow equations
AI总结：
本文针对CGL各向异性等离子体流动方程，通过重写方程消除非守恒项对熵的贡献，并借鉴MHD的Godunov对称化方法，设计了熵稳定有限差分格式，证明了半离散熵稳定性并通过数值实验验证了方法的有效性。
摘要：
本文研究Chew, Goldberger & Low (CGL)等离子体流动方程，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。这些方程在压力演化中采用了双绝热近似，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。我们首先对弱解进行了熵分析，然后为CGL方程提出了熵稳定有限差分格式。核心思想是重写CGL方程，使非守恒项不对熵方程产生贡献。重写后方程的守恒部分与磁流体力学(MHD)方程非常相似。随后，我们按照Godunov针对MHD的对称化过程对守恒部分进行对称化处理。基于守恒部分的熵缩放特征向量，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。我们证明了所提格式对于CGL方程的半离散熵稳定性。最后，利用由相应MHD测试算例导出的若干测试问题对格式进行了验证。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
