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

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.This research was supported by National Space Laboratory (NSL: S10801000121-08A0100-12110) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science, and Technology