2020/01/13 by Yize Yu, Yan Jiang, Yu, Yize +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #Computer science #Conservation law #Curvilinear coordinates #Divergence (linguistics) #FOS: Mathematics #FOS: Physical sciences #Finite difference #Finite difference method #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Geometry #Ideal (ethics) #Law #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamics #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear system #Numerical Analysis (math.NA) #Physics #Polygon mesh #cs.NA #math.NA #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.2001.04091
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/01/13 · openalex publication_date 2020/01/13 · arxiv updated 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.