TY - JOUR
T1 - Locally Divergence-Free Spectral-DG Methods for Ideal Magnetohydrodynamic Equations on Cylindrical Coordinates
AU - Yong Liu, Qingyuan Liu, Yuan Liu, Chi-Wang Shu & Mengping Zhang
JO - Communications in Computational Physics
VL - 3
SP - 631
EP - 653
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0187
UR - https://global-sci.org/intro/article_detail/cicp/13140.html
KW - Discontinuous Galerkin method, magnetohydrodynamics (MHD), divergence-free,
cylindrical coordinates.
AB - <p style="text-align: justify;">In this paper, we propose a class of high order locally divergence-free
spectral-discontinuous Galerkin (DG) methods for three dimensional (3D) ideal magnetohydrodynamic (MHD) equations on cylindrical geometry. Under the conventional
cylindrical coordinates (r,ϕ,z), we adopt the Fourier spectral method in the ϕ-direction
and discontinuous Galerkin (DG) approximation in the (r,z) plane, motivated by the
structure of the particular physical flows of magnetically confined plasma. By a careful
design of the locally divergence-free set for the magnetic filed, our spectral-DG methods are divergence-free inside each element for the magnetic field. Numerical examples with third order strong-stability-preserving Runge-Kutta methods are provided
to demonstrate the efficiency and performance of our proposed methods.</p>