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  

作　　者：Shijun Zou Xijun Yu Zihuan Dai Fang Qing Xiaolong Zhao 

机构地区：[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

出　　处：《Advances in Applied Mathematics and Mechanics》2023年第4期932-963,共32页应用数学与力学进展（英文）

基　　金：supported by National Natural Science Foundation of China(Nos.12071046,11671049,91330107,11571002 and 11702028);China Postdoctoral Science Foundation(No.2020TQ0013).

摘　　要：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.

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

分 类 号：O241[理学—计算数学]