JOURNAL OF COMPUTATIONAL PHYSICS | 卷:428 |
A constrained transport divergence-free finite element method for incompressible MHD equations | |
Article | |
Li, Lingxiao1  Zhang, Donghang2  Zheng, Weiying3,4  | |
[1] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China | |
[2] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China | |
[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC,NCMIS, Beijing 100190, Peoples R China | |
[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China | |
关键词: Magnetohydrodynamic equations; Constrained transport; Magnetic vector potential; Divergence-free finite element method; Block preconditioner; | |
DOI : 10.1016/j.jcp.2020.109980 | |
来源: Elsevier | |
【 摘 要 】
In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method, we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom. A comparison with other discretization using lid driven cavity is also given. (c) 2020 Elsevier Inc. All rights reserved.
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