A novel flux splitting based on wave-particle splitting for ideal magnetohydrodynamics

Abstract

A novel flux splitting method based on wave-particle splitting is developed for one-dimensional ideal magnetohydrodynamics. While ideal magnetohydrodynamics (MHD) equations are non-convex with non-homogeneous flux as opposed to their hydrodynamic counterparts, the present flux splitting methods cannot develop Riemann solver. The proposed approach based on wave-particle method referred as Advection Magnetic-direction Wave Particle Splitting (AMWPS) scheme splits the flux into four parts: the wave-like total pressure part, the wave-like normal magnetic part, the particle-like advection part and the particle-like tangential magnetic part. The particle-like parts can be solved by the scheme developed by Toro and Vazquez-Cendon (TV scheme) and we propose a novel approach to the solution of Riemann problem formed by the wave-like parts including total pressure sub-flux and normal magnetic sub-flux. As for the ordered wave foliation in MHD and other limitations in wave structure, we also analyze the relation between plasma β and specific heat ratio γ. The advantage of AMWPS is that it can sharply capture isolated, stationary Alfven wave discontinuity. Several one-dimensional and two-dimensional MHD problems have been tested to highlight the accuracy, positivity preservation and robustness of AMWPS scheme and comparative studies show that AMWPS significantly outperforms the Riemann solver named Harten, Lax and Leer for contact wave (HLLC) in most cases.