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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 Publication COMPUTERS & FLUIDS ISSN 0045-7930 Volume 42Issue:1Pages:54-61 Abstract We 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. Keyword Two-phase flow Phase field model Incompressible Navier-Stokes equations Artificial compressibility WENO scheme DOI 10.1016/j.compfluid.2010.10.021 Language 英语 Funding Project Natural 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 Area Computer Science ; Mechanics WOS Subject Computer Science, Interdisciplinary Applications ; Mechanics WOS ID WOS:000287285200006 Publisher PERGAMON-ELSEVIER SCIENCE LTD Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/11748 Collection 计算数学与科学工程计算研究所 Corresponding Author Shah, Abdullah Affiliation 1.COMSATS Inst Informat Technol, Dept Math, Islamabad 44000, Pakistan2.Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 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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