A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:278

Article

Zhao, Xuan¹  Yang, Yang²  Seyler, Charles E.¹ 

[1] Cornell Univ, Sch Elect & Comp Engn, Ithaca, NY 14853 USA

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

关键词: Positivity-preserving;    Discontinuous Galerkin;    Relaxation method;    Magnetohydrodynamics;    Two-fluid;    HED plasma;   

DOI  :  10.1016/j.jcp.2014.08.044

来源: Elsevier

【 摘 要 】

A positivity-preserving discontinuous Galerkin (DG) scheme [42] is used to solve the Extended Magnetohydrodynamics (XMHD) model, which is a two-fluid model expressed with a center-of-mass formulation. We prove that DG scheme with a positivity-preserving limiter is stable for the system governed by the XMHD model or the resistive MHD model. We use the relaxation system formulation [28] for describing the XMHD model, and solve the equations using a split level implicit-explicit time advance scheme, stepping over the time step constraint imposed by the stiff source terms. The magnetic field is represented in an exact locally divergence-free form of DG [23], which greatly improves the accuracy and stability of MHD simulations. As presently constructed, the method is able to handle a wide range of density variations, solve XMHD model on MHD time scales, and provide greatly improved accuracy over a Finite Volume implementation of the same model. (C) 2014 The Authors. Published by Elsevier Inc.

【 授权许可】

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