Locally Divergence-Free Spectral-DG Methods for Ideal Magnetohydrodynamic Equations on Cylindrical Coordinates
Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0187
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 631–653
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Discontinuous Galerkin method magnetohydrodynamics (MHD) divergence-free cylindrical coordinates.