Locally Divergence-Free Spectral-DG Methods for Ideal Magnetohydrodynamic Equations on Cylindrical Coordinates

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.