A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes
Abstract
A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) 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 HLL-type solvers, is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems. In particular, a HLLD solver on Cartesian meshes is extended to curvilinear meshes with proper modifications. A numerical boundary condition for the perfect electrical conductor (PEC) 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.
Keywords
Cite
@article{arxiv.1711.07415,
title = {A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes},
author = {Andrew J. Christlieb and Xiao Feng and Yan Jiang and Qi Tang},
journal= {arXiv preprint arXiv:1711.07415},
year = {2018}
}