Quasi-Gasdynamic Approach for Numerical Solution of Magnetohydrodynamic Equations

TL;DR

This paper presents a novel application of the Quasi-Gasdynamic method to solve ideal magnetohydrodynamic equations, enabling accurate modeling of compressible conductive gas flows with divergence-free magnetic fields.

Contribution

It introduces a quasi-gas-dynamic approach for MHD equations with a divergence-free magnetic field, verified through extensive 1D and 2D tests.

Findings

Method achieves high accuracy and convergence.

Ensures divergence-free magnetic field evolution.

Validated on standard test cases.

Abstract

We introduce an application of the Quasi-Gasdynamic method for a solution of ideal magnetohydrodynamic equations in the modeling of compressible conductive gas flows. A time-averaging procedure is applied for all physical parameters in order to obtain the quasi-gas-dynamic system of equations for magnetohydrodynamics. Evolution of all physical variables is presented in an unsplit divergence form. Divergence-free evolution of the magnetic field is provided by using a constrained transport method based on Stokes theorem. Accuracy and convergence of this method are verified on a large set of standard 1D and 2D test cases.