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Title of article :
Positivity-preserving DG and central DG methods for ideal MHD equations
Author/Authors :
Cheng، نويسنده , , Yue and Li، نويسنده , , Fengyan and Qiu، نويسنده , , Jianxian and Xu، نويسنده , , Liwei، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
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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.
Keywords :
MHD equations , Discontinuous Galerkin Method , Positivity-preserving , Central discontinuous Galerkin method , High order accuracy
Journal title :
Journal of Computational Physics
Journal title :
Journal of Computational Physics
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