An extension of gas-kinetic BGK Navier-Stokes scheme to multidimensional astrophysical magnetohydrodynamics

TL;DR

This paper extends a gas-kinetic scheme for Navier-Stokes equations to include magnetic fields, enabling accurate multidimensional simulations of astrophysical magnetohydrodynamics with improved stability and applicability to complex flows.

Contribution

It introduces a novel extension of the BGK Navier-Stokes scheme to resistive magnetic flows, incorporating magnetic effects into the gas-kinetic framework for astrophysical applications.

Findings

Validated with shock wave tests in 1D and 2D.

Successfully simulated 3D turbulent magneto-convection.

Enhanced scheme stability and accuracy for complex flows.

Abstract

The multidimensional gas-kinetic scheme for the Navier-Stokes equations under gravitational fields [J. Comput. Phys. 226 (2007) 2003-2027] is extended to resistive magnetic flows. The non-magnetic part of the magnetohydrodynamics equations is calculated by a BGK solver modified due to magnetic field. The magnetic part is treated by the flux splitting method based gas-kinetic theory [J. Comput. Phys. 153 (1999) 334-352 ], using a particle distribution function constructed in the BGK solver. To include Lorentz force effects into gas evolution stage is very important to improve the accuracy of the scheme. For some multidimensional problems, the deviations tangential to the cell interface from equilibrium distribution are essential to keep the scheme robust and accurate. Besides implementation of a TVD time discretization scheme, enhancing the dynamic dissipation a little bit is a simply and efficient way to stabilize the calculation. One-dimensional and two-dimensional shock waves tests are calculated to validate this new scheme. A three-dimensional turbulent magneto-convection simulation is used to show the applicability of current scheme to complicated astrophysical flows.