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• W2098364742 abstract "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 ρ 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." @default.
• W2098364742 created "2016-06-24" @default.
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• W2098364742 date "2013-04-01" @default.
• W2098364742 modified "2023-10-14" @default.
• W2098364742 title "Positivity-preserving DG and central DG methods for ideal MHD equations" @default.
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• W2098364742 doi "https://doi.org/10.1016/j.jcp.2012.12.019" @default.
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