@Article{AAMM-15-4,
author = {Zou, Shijun and Yu, Xijun and Zihuan, Dai and Qing, Fang and Zhao, Xiaolong},
title = {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},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {4},
pages = {932--963},
abstract = {<p style="text-align: justify;">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 $z$-component 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0366},
url = {https://global-sci.com/article/72860/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}
}