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The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers
Zhang, Lin1; Ouyang, Jie2; Zhang, Xiaohua3
2013-04-01
Source PublicationCOMPUTER PHYSICS COMMUNICATIONS
Volume184Issue:4Pages:1106-1118
AbstractThe aim of the paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics (MHD) flow problems with either fully insulating walls or partially insulating and partially conducting walls. Toward this, we first extend the influence domain of the shape function for the element free Galerkin (EFG) method to have arbitrary shape. When the influence factor approaches 1, we find that the EFG shape function almost has the Delta property at the node (i.e. the value of the EFG shape function of the node is nearly equal to 1 at the position of this node) as well as the property of slices in the influence domain of the node (i.e. the EFG shape function in the influence domain of the node is nearly constructed by different functions defined in different slices). Therefore, for MHO flow problems at high Hartmann numbers we follow the idea of the variational multiscale finite element method (VMFEM) to combine the EFG method with the variational multiscale (VM) method, namely the variational multiscale element free Galerkin (VMEFG) method is proposed. Subsequently, in order to validate the proposed method, we compare the obtained approximate solutions with the exact solutions for some problems where such exact solutions are known. Finally, several benchmark problems of MHD flows are simulated and the numerical results indicate that the VMEFG method is stable at moderate and high values of Hartmann number. Another important feature of this method is that the stabilization parameter has appeared naturally via the solution of the fine scale problem. Meanwhile, because this proposed method is a type of meshless method, it can avoid the need for meshing, a very demanding task for complicated geometry problems. (C) 2012 Elsevier B.V. All rights reserved.
KeywordMhd Flows Efg Vm Hartmann Number
SubtypeArticle
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
Indexed BySCI
Language英语
WOS KeywordTRANSVERSE MAGNETIC-FIELD ; FINITE-ELEMENT ; MAGNETOHYDRODYNAMIC FLOW ; EQUATION ; BUBBLES ; PIPE
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000315974100004
Citation statistics
Cited Times:24[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.ipe.ac.cn/handle/122111/13669
Collection研究所(批量导入)
Affiliation1.Chinese Acad Sci, Inst Proc Engn, State Key Lab Multiphase Complex Syst, Beijing 100190, Peoples R China
2.Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Peoples R China
3.China Three Gorges Univ, Coll Sci, Yichang 443002, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Lin,Ouyang, Jie,Zhang, Xiaohua. The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers[J]. COMPUTER PHYSICS COMMUNICATIONS,2013,184(4):1106-1118.
APA Zhang, Lin,Ouyang, Jie,&Zhang, Xiaohua.(2013).The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers.COMPUTER PHYSICS COMMUNICATIONS,184(4),1106-1118.
MLA Zhang, Lin,et al."The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers".COMPUTER PHYSICS COMMUNICATIONS 184.4(2013):1106-1118.
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