@Article{CiCP-26-631, author = {}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0187}, url = {http://global-sci.org/intro/article_detail/cicp/13140.html} }