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The multidimensional gas-kinetic scheme for the Navier-Stokes equations undergravitational fields [J. Comput. Phys. 226 (2007) 2003-2027] is extended toresistive magnetic flows. The non-magnetic part of the magnetohydrodynamicsequations is calculated by a BGK solver modified due to magnetic field. Themagnetic part is treated by the flux splitting method based gas-kinetic theory[J. Comput. Phys. 153 (1999) 334-352 ], using a particle distribution functionconstructed in the BGK solver. To include Lorentz force effects into gasevolution stage is very important to improve the accuracy of the scheme. Forsome multidimensional problems, the deviations tangential to the cell interfacefrom equilibrium distribution are essential to keep the scheme robust andaccurate. Besides implementation of a TVD time discretization scheme, enhancingthe dynamic dissipation a little bit is a simply and efficient way to stabilizethe calculation. One-dimensional and two-dimensional shock waves tests arecalculated to validate this new scheme. A three-dimensional turbulentmagneto-convection simulation is used to show the applicability of currentscheme to complicated astrophysical flows.

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