A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field

Zou，Shijun1; Yu，Xijun2; Dai，Zihuan2; Qing，Fang3; Zhao，Xiaolong4

2023-08-01

10.4208/aamm.OA-2021-0366

Advances in Applied Mathematics and Mechanics   影响因子和分区

2070-0733

2075-1354

A partial Runge-Kutta Discontinuous Galerkin (RKDG) method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics (MHD) equations written in semi-Lagrangian formulation on moving quadrilateral meshes. In this method, the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper [47]. The numerical magnetic field in the remaining two directions (i.e., x and y) are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD. Since the divergence of the magnetic field in 2D is independent of its z-direction component, an exactly divergence-free numerical magnetic field can be obtained by this treatment. We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes. A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations. Some numerical examples are presented to demonstrate the accuracy, non-oscillatory property and preservation of the exactly divergence-free property of our method.

exactly divergence-free magnetic field Ideal compressible MHD equations Runge-Kutta discontinuous Galerkin method semi-Lagrangian formulation

SCI

英语

其他

National Natural Science Foundation of China[11571002];National Natural Science Foundation of China[11671049];National Natural Science Foundation of China[11702028];National Natural Science Foundation of China[12071046];China Postdoctoral Science Foundation[2020TQ0013];National Natural Science Foundation of China[91330107];

Mathematics ; Mechanics

Mathematics, Applied ; Mechanics

WOS:000976963900005

GLOBAL SCIENCE PRESS

2-s2.0-85159581693

Scopus

1.School of Mathematical Sciences,Peking University,Beijing,100871,China
2.Institute of Applied Physics and Computational Mathematics,Beijing,100088,China
3.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
4.School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,Henan,450001,China

Zou，Shijun,Yu，Xijun,Dai，Zihuan,et al. A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field[J]. Advances in Applied Mathematics and Mechanics,2023,15(4):932-963.

Zou，Shijun,Yu，Xijun,Dai，Zihuan,Qing，Fang,&Zhao，Xiaolong.(2023).A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field.Advances in Applied Mathematics and Mechanics,15(4),932-963.

Zou，Shijun,et al."A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field".Advances in Applied Mathematics and Mechanics 15.4(2023):932-963.