A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field  

作　　者：Shijun Zou Xiaolong Zhao Xijun Yu Zihuan Dai 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,P.R.China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,P.R.China [3]Institute of Applied Physics and Computational Mathematics,Beijing 100088,P.R.China

出　　处：《Communications in Computational Physics》2022年第7期547-582,共36页计算物理通讯（英文）

基　　金：supported by National Natural Science Foundation of China(12071046,11671049,91330107,11571002 and 11702028);China Postdoctoral Science Foundation(2020TQ0013).

摘　　要：In this paper,we present a Runge-Kutta Discontinuous Galerkin(RKDG)method for solving the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations under the Lagrangian framework.The fluid part of the ideal MHD equations along with z-component of the magnetic induction equation are discretized using a DG method based on linear Taylor expansions.By using the magnetic fluxfreezing principle which is the integral form of the magnetic induction equation of the ideal MHD,an exactly divergence-free numerical magnetic field can be obtained.The nodal velocities and the corresponding numerical fluxes are explicitly calculated by solving multidirectional approximate Riemann problems.Two kinds of limiter are proposed to inhibit the non-physical oscillation around the shock wave,and the second limiter can eliminate the phenomenon of mesh tangling in the simulations of the rotor problems.This Lagrangian RKDG method conserves mass,momentum,and total energy.Several numerical tests are presented to demonstrate the accuracy and robustness of the proposed scheme.

关 键 词：Lagrangian RKDG method ideal compressible MHD equations Taylor basis exactly divergence-freemagnetic field LIMITER 

分 类 号：O17[理学—数学]