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Chin. Phys. B, 2012, Vol. 21(12): 124703    DOI: 10.1088/1674-1056/21/12/124703
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

Xie Hai-Qiong (谢海琼)a, Zeng Zhong (曾忠)a b c, Zhang Liang-Qi (张良奇)a, Liang Gong-You (梁功有)a, Hiroshi Mizusekic, Yoshiyuki Kawazoec
a Department of Engineering Mechanics, Chongqing University, Chongqing 400044, China;
b State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China;
c Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
Abstract  In this paper, an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with sharp interface, where the surface tension is implemented. The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid, an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface, and an indicator function is introduced to update accurately the fluid properties. The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points, and then the surface tension is directly computed by using the normal vector and curvature of the interface. Two benchmark problems, including the Laplace's law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation. Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.
Keywords:  lattice Boltzmann method      multi-relaxation-time      front tracking method      surface tension      two-phase flow  
Received:  11 May 2012      Revised:  05 June 2012      Accepted manuscript online: 
PACS:  47.61.Jd (Multiphase flows)  
  47.11.-j (Computational methods in fluid dynamics)  
  47.45.Ab (Kinetic theory of gases)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10872222 and 50921063), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110191110037), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. CDJXS11240011 and CDJXS10241103).
Corresponding Authors:  Zeng Zhong     E-mail:  zzeng@cqu.edu.cn

Cite this article: 

Xie Hai-Qiong (谢海琼), Zeng Zhong (曾忠), Zhang Liang-Qi (张良奇), Liang Gong-You (梁功有), Hiroshi Mizuseki, Yoshiyuki Kawazoe Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension 2012 Chin. Phys. B 21 124703

[1] Hirt C W and Nichols B D 1981 J. Comput. Phys. 39 201
[2] Ruschak K J 1980 Int. J. Numer. Methods Eng. 15 639
[3] Sussman M, Smereka P and Osher S 1994 J. Comput. Phys. 114 146
[4] Chen S and Doolen G D 1998 Ann. Rev. Fluid Mech. 30 329
[5] Gunstensen A K, Rothman D H, Zaleski S and Zanetti G 1991 Phys. Rev. A 43 4320
[6] Shan X W and Chen H D 1993 Phys. Rev. E 47 1815
[7] Swift M R, Orlandini E, Osborn W R and Yeomans J M 1996 Phys. Rev. E 54 5041
[8] Yi H H, Yang X F, Wang C F and Li H B 2009 Chin. Phys. B 18 2878
[9] Yi H H, Fan L J, Yang X F and Li H B 2009 Chin. Phys. Lett. 26 048701
[10] Cai J and Huai X L 2009 Chin. Phys. Lett. 26 064401
[11] Zhong C W, Xie J F, Zhou C S, Xiong S W and Yin D C 2009 Chin. Phys. B 18 4083
[12] Ran Z 2009 Chin. Phys. B 18 2159
[13] Lallemand P, Luo L S and Peng Y 2007 J. Comput. Phys. 226 1367
[14] Peskin C S 1977 J. Comput. Phys. 25 220
[15] Tryggvason G, Bunner B, Esmaeeli A, Juric D, Rawahi N, Tauber W, Han J, Nas S and Jan Y J 2001 J. Comput. Phys. 169 708
[16] Unverdi S O and Tryggvason G 1992 J. Comput. Phys. 100 25
[17] He X Y and Luo L S 1997 J. Stat. Phys. 88 927
[18] Lallemand P and Luo L S 2000 Phys. Rev. E 61 6546
[19] D'Humières D 1992 Progress in Astronautics and Aeronauttics 159 450
[20] Guo Z L and Zheng C G 2008 Int. J. Comput. Fluid Dyn. 22 465
[21] Popinet S and Zaleski S 1999 Int. J. Numer. Methods Fulids 30 775
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