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.

翻译：本文提出了一种求解描述磁场中双麦克斯韦等离子体的Chew-Goldberger-Low（CGL）方程组的新型数值模型。日球层和地球空间环境常被观测到处于各向异性状态，其平行与垂直压力分量存在显著差异。CGL方程组是对常见各向同性磁流体动力学（MHD）模型的最简一阶修正，同时保留了后者最理想的特性。然而，CGL方程组存在若干数值挑战：该系统不具守恒形式，源项具有刚性，且与MHD不同，当平行与垂直压力差异过大时系统可能失去双曲性。常规解决方案是使平行与垂直压力相互趋近，但该方法通常依赖特定假设。我们提出一种基于投掷角散射思想的物理信息压力弛豫方法，既能保持数值系统的双曲特性，又能在等离子体β值极大时自然趋近于零各向异性。基于CGL方程组的数值代码因此能够在任意磁场强度下稳定运行，包括磁场趋近于零的极限情况。我们通过若干严格测试问题展示了新算法的性能，这些测试对比了CGL方程组在弱碰撞与强碰撞极限下的表现，其中包括模拟二维激波与磁层环境相互作用的测试案例。