TY - JOUR
T1 - 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
AU - Zou , Shijun
AU - Yu , Xijun
AU - Dai , Zihuan
AU - Qing , Fang
AU - Zhao , Xiaolong
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 932
EP - 963
PY - 2023
DA - 2023/04
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0366
UR - https://global-sci.org/intro/article_detail/aamm/21597.html
KW - Ideal compressible MHD equations, semi-Lagrangian formulation, exactly divergence-free magnetic field, Runge-Kutta discontinuous Galerkin method.
AB - <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>