TY - JOUR
T1 - A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field
AU - Zou , Shijun
AU - Zhao , Xiaolong
AU - Yu , Xijun
AU - Dai , Zihuan
JO - Communications in Computational Physics
VL - 2
SP - 547
EP - 582
PY - 2022
DA - 2022/08
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2021-0130
UR - https://global-sci.org/intro/article_detail/cicp/20868.html
KW - Lagrangian RKDG method, ideal compressible MHD equations, Taylor basis, exactly divergence-free magnetic field, limiter.
AB - <p style="text-align: justify;">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.</p>