Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes
| Autor: | Yan Jiang, Yize Yu, Mengping Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Physical sciences
01 natural sciences Mathematics::Numerical Analysis Theoretical Computer Science FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Divergence (statistics) Mathematics Numerical Analysis Curvilinear coordinates Conservation law Ideal (set theory) Applied Mathematics General Engineering Finite difference Numerical Analysis (math.NA) Computational Physics (physics.comp-ph) 010101 applied mathematics Computational Mathematics Nonlinear system Computational Theory and Mathematics Magnetic potential Magnetohydrodynamics Physics - Computational Physics Software |
| Popis: | 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 (Christlieb et al. in SIAM J Sci Comput 40(4):A2631–A2666, 2018) 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. |
| Databáze: | OpenAIRE |
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