Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 238, Issue -, Pages 255-280Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.12.019
Keywords
MHD equations; Discontinuous Galerkin method; Central discontinuous Galerkin method; Positivity-preserving; High order accuracy
Funding
- NSF [DMS-0652481, DMS-0636358]
- NSF CAREER award [DMS-0847241]
- NSF of China [10931004]
- ISTCP of China [2010DFR00700]
- Alfred P. Sloan Research Fellowship
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0847241] Funding Source: National Science Foundation
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Ideal MHD equations arise in many applications such as astrophysical plasmas and space physics, and they consist of a system of nonlinear hyperbolic conservation laws. The exact density rho and pressure p should be non-negative. Numerically, such positivity property is not always satisfied by approximated solutions. One can encounter this when simulating problems with low density, high Mach number, or much large magnetic energy compared with internal energy. When this occurs, numerical instability may develop and the simulation can break down. In this paper, we propose positivity-preserving discontinuous Galerkin and central discontinuous Galerkin methods for solving ideal MHD equations by following [X. Zhang, C.-W. Shu, Journal of Computational Physics 229 (2010) 8918-8934]. In one dimension, the positivity-preserving property is established for both methods under a reasonable assumption. The performance of the proposed methods, in terms of accuracy, stability and positivity-preserving property, is demonstrated through a set of one and two dimensional numerical experiments. The proposed methods formally can be of any order of accuracy. (C) 2013 Elsevier Inc. All rights reserved.
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