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arXiv · 1711.07415

A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes

Andrew J. Christlieb·Xiao Feng·Yan Jiang·Qi Tang
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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.

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Andrew J. Christlieb, Xiao Feng, Yan Jiang, Qi Tang. 2017-11-20. A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes. https://arxiv.org/abs/1711.07415

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