A hybrid scheme for compressible magnetohydrodynamic turbulence

An efficient, high-resolution and oscillation-free hybrid scheme for shock-turbulence interactions in compressible magnetohydrodynamic (MHD) problems is presented. The hybrid scheme couples a sixth-order compact finite difference scheme in the smooth regions with a fifth-order WENO scheme in the shock regions. An eighth-order pentadiagonal filter is derived and utilized to maintain numerical stability and eliminate spurious oscillations. Various numerical examples are presented and the hybrid algorithm is proved to be accurate for smooth solutions and be able to capture discontinuities robustly. We have also shown the good capability of the hybrid scheme for the compressible MHD turbulence.