Development of Genuinely Multidimensional Upwind Residual Distribution Schemes for the System of Eight Wave Ideal Magnetohydro-Dynamic Equations on Unstructured Grids

Abstract

Multidimensional upwind residual distribution schemes are applied to the eight-wave equations of ideal magnetohydrodynamics. Both first and second order linear, and second order nonlinear distribution schemes are presented. The solenoidal condition of the magnetic field is enforced by Powell’s source term approach. Time integration is done by using both explicit and implicit strategies. The spatial accuracy and the shock capturing properties of the schemes in the steady state are investigated numerically. Computational results are shown for a super-magnetosonic channel flow.