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Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility
Shah, Abdullah1; Yuan, Li2,3
2011-03-01
Source PublicationCOMPUTERS & FLUIDS
ISSN0045-7930
Volume42Issue:1Pages:54-61
AbstractWe present an artificial compressibility based numerical method for a phase field model for simulating two-phase incompressible viscous flows. The phase model was proposed by Liu and Shen [Physica D. 179 (2003) 211-228], in which the interface between two fluids is represented by a thin transition region of fluid mixture that stores certain amount of mixing energy. The model consists of the Navier-Stokes equations coupled with the Allen-Cahn equation (phase field equation) through an extra stress term and a transport term. The extra stress in the momentum equations represents the phase-induced capillary effect for the mixture due to the surface tension. The coupled equations are cast into a conservative form suitable for implementation with the artificial compressibility method. The resulting hyperbolic system of equations are then discretized with weighted essentially non-oscillatory (WENO) finite difference scheme. The dual-time stepping technique is applied for obtaining time accuracy at each physical time step, and the approximate factorization algorithm is used to solve the discretized equations. The effectiveness of the numerical method is demonstrated in several two-phase flow problems with topological changes. Numerical results show the present method can be used to simulate incompressible two-phase flows with small interfacial width parameters and topological changes. (C) 2010 Elsevier Ltd. All rights reserved.
KeywordTwo-phase flow Phase field model Incompressible Navier-Stokes equations Artificial compressibility WENO scheme
DOI10.1016/j.compfluid.2010.10.021
Language英语
Funding ProjectNatural Science Foundation of China[10729101] ; Natural Science Foundation of China[10972230] ; state key program for developing basic sciences[2005CB321703] ; state key program for developing basic sciences[2010CB731505]
WOS Research AreaComputer Science ; Mechanics
WOS SubjectComputer Science, Interdisciplinary Applications ; Mechanics
WOS IDWOS:000287285200006
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/11748
Collection计算数学与科学工程计算研究所
Corresponding AuthorShah, Abdullah
Affiliation1.COMSATS Inst Informat Technol, Dept Math, Islamabad 44000, Pakistan
2.Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
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Shah, Abdullah,Yuan, Li. Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility[J]. COMPUTERS & FLUIDS,2011,42(1):54-61.
APA Shah, Abdullah,&Yuan, Li.(2011).Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility.COMPUTERS & FLUIDS,42(1),54-61.
MLA Shah, Abdullah,et al."Numerical solution of a phase field model for incompressible two-phase flows based on artificial compressibility".COMPUTERS & FLUIDS 42.1(2011):54-61.
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