A constrained transport divergence-free finite element method for incompressible MHD equations

doi:10.1016/j.jcp.2020.109980

	A constrained transport divergence-free finite element method for incompressible MHD equations
	Li, Lingxiao 2; Zhang, Donghang 3; Zheng, Weiying 1,4
刊名	JOURNAL OF COMPUTATIONAL PHYSICS
	2021-03-01
卷号	428 页码:22
关键词	Magnetohydrodynamic equations Constrained transport Magnetic vector potential Divergence-free finite element method Block preconditioner
ISSN号	0021-9991
DOI	10.1016/j.jcp.2020.109980
英文摘要	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.
资助项目	National Natural Science Foundation of China[11901042] ; National Science Fund for Distinguished Young Scholars[11725106] ; China NSF grant[11831016]
WOS研究方向	Computer Science ; Physics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000612233800013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58173]
专题	中国科学院数学与系统科学研究院
通讯作者	Zheng, Weiying
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC,NCMIS, Beijing 100190, Peoples R China 2.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 3.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Lingxiao,Zhang, Donghang,Zheng, Weiying. A constrained transport divergence-free finite element method for incompressible MHD equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2021,428:22.
APA	Li, Lingxiao,Zhang, Donghang,&Zheng, Weiying.(2021).A constrained transport divergence-free finite element method for incompressible MHD equations.JOURNAL OF COMPUTATIONAL PHYSICS,428,22.
MLA	Li, Lingxiao,et al."A constrained transport divergence-free finite element method for incompressible MHD equations".JOURNAL OF COMPUTATIONAL PHYSICS 428(2021):22.