Gas Kinetic Schemes for Solving the Magnetohydrodynamic Equations with Pressure Anisotropy

TL;DR

This paper introduces a robust gas-kinetic numerical scheme for solving anisotropic magnetohydrodynamic equations, effectively handling plasma systems with pressure anisotropy common in astrophysics.

Contribution

It develops a novel gas-kinetic flux scheme specifically designed for anisotropic MHD equations, suitable for finite-volume solvers and extendable to complex plasma models.

Findings

Scheme performs well on linear wave problems

Scheme is robust for non-linear MHD simulations

Applicable to multi-fluid and generalized plasma systems

Abstract

In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are needed to describe such a plasma system. To solve the anisotropic MHD equation numerically, we develop a robust Gas-Kinetic flux scheme for non-linear MHD flows. Using anisotropic velocity distribution functions, the numerical flux functions are derived for updating the macroscopic plasma variables. The schemes is suitable for finite-volume solvers which utilize a conservative form of the mass, momentum and total energy equations, and can be easily applied to multi-fluid problems and extended to more generalized double polytropic plasma systems. Test results show that the numerical scheme is very robust and performs well for both linear wave and non-linear MHD problems.