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Simulating Magnetohydrodynamic Instabilities with Conservative Perturbed MHD Model Using Discontinuous Galerkin Method

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Astronomy and astrophysics (General)

Published online by Cambridge University Press:  27 March 2017

Jun Ma ,
Wenfeng Guo  and
Zhi Yu
Jun Ma*
Affiliation:
Institute of Plasma Physics, Chinese Academy of sciences, Hefei 230031, China Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031, China
Wenfeng Guo*
Affiliation:
Institute of Plasma Physics, Chinese Academy of sciences, Hefei 230031, China Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031, China
Zhi Yu*
Affiliation:
Institute of Plasma Physics, Chinese Academy of sciences, Hefei 230031, China Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031, China
*
*Corresponding author. Email addresses:junma@ipp.ac.cn (J. Ma), wfguo@ipp.ac.cn (W. Guo), yuzhi@ipp.ac.cn (Z. Yu)
*Corresponding author. Email addresses:junma@ipp.ac.cn (J. Ma), wfguo@ipp.ac.cn (W. Guo), yuzhi@ipp.ac.cn (Z. Yu)
*Corresponding author. Email addresses:junma@ipp.ac.cn (J. Ma), wfguo@ipp.ac.cn (W. Guo), yuzhi@ipp.ac.cn (Z. Yu)
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Abstract

In magnetically confined plasma research, the understandings of small and large perturbations at equilibrium are both critical for plasma controlling and steady state operation. Numerical simulations using original MHD model can hardly give clear picture for small perturbations, while non-conservative perturbed MHD model may break conservation law, and give unphysical results when perturbations grow large after long-time computation. In this paper, we present a nonlinear conservative perturbed MHD model by splitting primary variables in original MHD equations into equilibrium part and perturbed part, and apply an approach in the framework of discontinuous Galerkin (DG) spatial discretization for numerical solutions. This enables high resolution of very small perturbations, and also gives satisfactory non-smooth solutions for large perturbations, which are both broadly concerned in magnetically confined plasma research. Numerical examples demonstrate satisfactory performance of the proposed model clearly. For small perturbations, the results have higher resolution comparing with the original MHD model; for large perturbations, the non-smooth solutions match well with existing references, confirming reliability of the model for instability investigations in magnetically confined plasma numerical research.

Keywords

Discontinuous Galerkin methodconservative perturbed MHD model

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65Z05: Applications to physics 85-08: Computational methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1429 - 1448
Copyright
Copyright © Global-Science Press 2017 

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