Accurate and Robust Pressure Weight Advection Upstream Splitting Method for Magnetohydrodynamics Equations

Abstract

Two variants of the advection upstream splitting method are modified to solve the equations of ideal magnetohydrodynamics. Discontinuity-sensing functions used in AUSMPW and M-AUSMPW for the magnetohydrodynamics equations are newly defined in consideration of a magnetic field. The new pressure-based weight functions are shown to effectively remove the oscillations behind a strong shock wave as well as provide a highly accurate solution for a stationary contact discontinuity. To satisfy the divergence-free constraint of a magnetic field, the hyperbolic divergence cleaning method is chosen and applied for all the test cases. Ryu and Jones onedimensional magnetohydrodynamics shock-tube problem and Orszag and Tangs two-dimensional magnetohydrodynamics vortex system are evaluated to validate and show the advantages of the newly developed schemes.