标题： 超越MHD近似：基于物理的CGL方程数值解法 显示英文标题

标题： Going Beyond the MHD Approximation: Physics-Based Numerical Solution of the CGL Equations

摘要： 我们提出了一种新的数值模型，用于求解描述磁场中双麦克斯韦等离子体的Chew-Goldberger-Low方程组。日球和地球空间环境通常被观测到处于各向异性状态，具有明显不同的平行和垂直压力分量。CGL方程组是对常见各向同性MHD模型的最简单的主导阶修正，仍然允许纳入后者最具吸引力的特性。然而，CGL方程组存在几个数值挑战：该系统不是守恒形式，源项是刚性的，并且与MHD不同，如果平行和垂直压力变得过于不同，它容易失去双曲性。通常的解决方法是使平行和垂直压力更接近；但通常是以一种随意的方式进行的。我们提出了一种基于回旋角散射思想的物理信息压力松弛方法，该方法保持数值系统的双曲性，并在等离子体β非常大的极限下自然导致零各向异性。因此，基于CGL方程的数值代码可以针对任何磁场强度正常运行，包括磁场趋近于零的极限情况。我们的新算法的能力通过几个严格的测试问题得到演示，这些测试问题提供了弱碰撞和强碰撞极限下CGL方程的比较。这包括一个在二维情况下模拟冲击波与磁层环境相互作用的测试问题。 显示英文摘要

摘要： We present a new numerical model for solving the Chew-Goldberger-Low system of equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and geospace environments are often observed to be in an anisotropic state with distinctly different parallel and perpendicular pressure components. The CGL system represents the simplest leading order correction to the common isotropic MHD model that still allows to incorporate the latter's most desirable features. However, the CGL system presents several numerical challenges: the system is not in conservation form, the source terms are stiff, and unlike MHD it is prone to a loss of hyperbolicity if the parallel and perpendicular pressures become too different. The usual cure is to bring the parallel and perpendicular pressures closer to one another; but that has usually been done in an ad hoc manner. We present a physics-informed method of pressure relaxation based on the idea of pitch-angle scattering that keeps the numerical system hyperbolic and naturally leads to zero anisotropy in the limit of very large plasma beta. Numerical codes based on the CGL equations can, therefore, be made to function robustly for any magnetic field strength, including the limit where the magnetic field approaches zero. The capabilities of our new algorithm are demonstrated using several stringent test problems that provide a comparison of the CGL equations in the weakly and strongly collisional limits. This includes a test problem that mimics interaction of a shock with a magnetospheric environment in 2D.