@Article{CiCP-26-631,
author = {Yong Liu, Qingyuan Liu, Yuan Liu, Chi-Wang Shu and Mengping Zhang},
title = {Locally Divergence-Free Spectral-DG Methods for Ideal Magnetohydrodynamic Equations on Cylindrical Coordinates},
journal = {Communications in Computational Physics},
year = {2019},
volume = {26},
number = {3},
pages = {631--653},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0187},
url = {http://global-sci.org/intro/article_detail/cicp/13140.html}
}