A HIGH-ORDER FINITE DIFFERENCE WENO SCHEME FOR IDEAL MAGNETOHYDRODYNAMICS ON CURVILINEAR MESHES

摘要

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially nonoscillatory scheme. It computes a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher-order terms constructed from physical fluxes by limited central differences. The scheme coupled with several Riemann solvers, including a Lax-Friedrichs solver and Harten-Lax-van Leer type solvers, is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems. In particular, an HLLD (where D stands for discontinuities) solver on Cartesian meshes is extended to curvilinear meshes with proper modifications. A numerical boundary condition for the perfect electrical conductor boundary is derived for general geometry and verified through a bow shock flow. Numerical results also confirm the advantages of using low dissipative Riemann solvers in the current framework.