Gas-kinetic BGK scheme for three dimensional magnetohydrodynamics

The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J. Comput. Phys., 1999;2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter η is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.