A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field
Year: 2022
Author: Shijun Zou, Xiaolong Zhao, Xijun Yu, Zihuan Dai
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 547–582
Abstract
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 flux-freezing 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0130
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 547–582
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 36
Keywords: Lagrangian RKDG method ideal compressible MHD equations Taylor basis exactly divergence-free magnetic field limiter.
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