A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows

doi:10.1016/j.cma.2019.07.022

	A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows
	Yang, Jinjin 1,2; Mao, Shipeng3 ; He, Xiaoming 4; Yang, Xiaofeng 5; He, Yinnian 2
	2019-11-01
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	356 页码:435-464
摘要	In this paper, we propose a diffuse interface model and finite element approximation for two-phase magnetohydrodynamic (MHD) flows with different viscosities and electric conductivities. An energy stable scheme, which is based on the finite element method for the spatial discretization and first order semi-implicit scheme combined with convex splitting method for the temporal discretization, is proposed to solve this new model. The numerical scheme is proved to be mass-conservative and energy law preserving. By Leray-Schauder fixed point theorem, the existence of solutions to the numerical scheme is shown. The uniqueness of the numerical solutions is obtained. Utilizing the stability of the numerical scheme and the compactness method, the existence of the weak solutions to the two-phase MHD model is established as well. Furthermore, given more regularity on the weak solution, the convergence of the numerical scheme is derived. Finally, numerical experiments are provided to verify the theoretical results and validate the proposed model. (C) 2019 Published by Elsevier B.V.
关键词	Two-phase MHD flows Diffuse interface models Finite element method Energy stability Semi-implicit scheme
DOI	10.1016/j.cma.2019.07.022
语种	英语
资助项目	NSF, USA[DMS-1818642] ; NSF, USA[DMS-1818783] ; NSF of China[11871467] ; NSF of China[11771348] ; Youth Innovation Promotion Association of CAS[2016003]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000485835500017
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35618
专题	计算数学与科学工程计算研究所
通讯作者	He, Xiaoming
作者单位	1.Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450015, Henan, Peoples R China 2.Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China 3.Univ Chinese Acad Sci, Acad Math & Syst Sci, Chinese Acad Sci, Sch Math Sci,LSEC, Beijing 100190, Peoples R China 4.Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA 5.Univ South Carolina, Dept Math, Columbia, SC 29208 USA
推荐引用方式 GB/T 7714	Yang, Jinjin,Mao, Shipeng,He, Xiaoming,et al. A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2019,356:435-464.
APA	Yang, Jinjin,Mao, Shipeng,He, Xiaoming,Yang, Xiaofeng,&He, Yinnian.(2019).A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,356,435-464.
MLA	Yang, Jinjin,et al."A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 356(2019):435-464.