A High-Order Gas-Kinetic Method for Multidimensional Ideal Magnetohydrodynamics

This paper extends the gas-kinetic theory based flux splitting method for ideal magnetohydrodynamics (MHD) equations (K. Xu, 1999, J. Comput. Phys.153, 334) to multidimensional cases. The kinetic MHD scheme is constructed based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle “collisions” are implemented in the free transport process to reduce the numerical dissipation. The high-order resolution of the scheme is achieved through the MUSCL-type initial reconstruction and the Runge–Kutta time-stepping method. The numerical tests include the spherical explosion, the Kelvin–Helmholtz instability, and the Orszag–Tang MHD turbulence problems. Numerical results validate the accuracy of the kinetic approach.