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arXiv · 2001.04091

Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes

Yize Yu·Yan Jiang·Mengping Zhang
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Abstract

In this paper, a high order free-stream preserving finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the ideal magnetohydrodynamic (MHD) equations on curvilinear meshes. Under the constrained transport framework, magnetic potential evolved by a Hamilton-Jacobi (H-J) equation is introduced to control the divergence error. In this work, we use the alternative formulation of WENO scheme [10] for the nonlinear hyperbolic conservation law, and design a novel method to solve the magnetic potential. Theoretical derivation and numerical results show that the scheme can preserve free-stream solutions of MHD equations, and reduce error more effectively than the standard finite difference WENO schemes for such problems.

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Yize Yu, Yan Jiang, Mengping Zhang. 2020-01-13. Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes. https://arxiv.org/abs/2001.04091

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