Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation
He Wang(王贺)1, Fang-Bao Tian(田方宝)2, and Xiang-Dong Liu(刘向东)1,3,†
1 Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China; 2 School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia; 3 College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China
Abstract A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen-Cahn equation (ACE). By adopting the improved form of a relaxation matrix and an equilibrium distribution function, the time derivative ∂t(φu) induced by recovering the diffusion term in ACE is eliminated. The conducted Chapman-Enskog analysis demonstrates that the correct conservative ACE is recovered. Four benchmark cases including Zalesak's disk rotation, vortex droplet, droplet impact on thin film, and Rayleigh-Taylor instability are investigated to validate the proposed model. The numerical results indicate that the proposed model can accurately describe the complex interface deformation.
Corresponding Authors:
Xiang-Dong Liu
E-mail: liuxd@yzu.edu.cn
Cite this article:
He Wang(王贺), Fang-Bao Tian(田方宝), and Xiang-Dong Liu(刘向东) Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation 2022 Chin. Phys. B 31 024701
[1] Dbouk T and Drikakis D 2020 Phys. Fluids32 053310 [2] Gao W and Chen Y 2019 Int. J. Heat Mass Tran.135 158 [3] Gerritsen M G and Durlofsky L J 2005 Annu. Rev. Fluid Mech.37 211 [4] Wu L Y, Liu L B, Han X T, Li Q W and Yang W B 2019 Chin. Phys. B28 104702 [5] Gao W, Yu C and Yao F 2020 Chin. Phys. B29 054702 [6] Gao Y J, Jiang H Q, Li J J, Zhao Y Y, Hu J C and Chang Y H 2017 Acta Phys. Sin.66 024702 (in Chinese) [7] Zhao K, She Y Z, Jiang Y L, Qin J and Zhang Z H 2019 Acta Phys. Sin.68 244401 (in Chinese) [8] Liu H, Zhang Y and Valocchi A J 2015 Phys. Fluids27 052103 [9] Ma J, Wang Z, Young J, Lai J C S, Sui Y and Tian F B 2020 J. Comput. Phys.415 109487 [10] Xu L, Tian F B, Young J and Lai J C S 2018 J. Comput. Phys.375 22 [11] Zhang Z D, Cao Y T, Sun D K, Xing H, Wang J C and Ni Z H 2020 Chin. Phys. B29 028103 [12] Gunstensen A K, Rothman D H, Zaleski S and Zanetti G 1991 Phys. Rev. A43 4320 [13] Liu H, Valocchi A J and Kang Q 2012 Phys. Rev. E85 069901 [14] Wen Z X, Li Q, Yu Y and Luo K H 2019 Phys. Rev. E100 023301 [15] Inamuro T, Konishi N and Ogino F 2000 Comput. Phys. Commun.129 32 [16] Pooley C M and Furtado K 2008 Phys. Rev. E77 046702 [17] Swift M R, Orlandini E, Osborn W R and Yeomans J M 1996 Phys. Rev. E54 5041 [18] Li Q, Luo K H and Li X J 2013 Phys. Rev. E87 053301 [19] Shan X W and Chen H D 1993 Phys. Rev. E47 1815 [20] Zhang Q Y, Sun D K and Zhu M F 2017 Chin. Phys. B26 084701 [21] Fakhari A and Rahimian M H 2010 Phys. Rev. E81 036707 [22] Geier M, Fakhari A and Lee T 2015 Phys. Rev. E91 063309 [23] He X Y, Chen S Y and Zhang R Y 1999 J. Comput. Phys.152 642 [24] Lee T and Lin C L 2005 J. Comput. Phys.206 16 [25] Liang H, Shi B C, Guo Z L and Chai Z H 2014 Phys. Rev. E89 053320 [26] Ren F, Song B, Sukop M C and Hu H 2016 Phys. Rev. E94 023311 [27] Zheng H W, Shu C and Chew Y T 2005 Phys. Rev. E72 056705 [28] Zheng H W, Shu C and Chew Y T 2006 J. Comput. Phys.218 353 [29] Zu Y Q and He S 2013 Phys. Rev. E87 043301 [30] Huang H, Huang J J, Lu X Y and Sukop M C 2013 Int. J. Mod. Phys. C24 1350021 [31] Chai Z, Sun D, Wang H and Shi B 2018 Int. J. Heat Mass Transfer122 631 [32] Wang H L, Chai Z H, Shi B C and Liang H 2016 Phys. Rev. E94 033304 [33] Liang H, Xu J, Chen J, Wang H, Chai Z and Shi B 2018 Phys. Rev. E97 033309 [34] Marié S, Ricot D and Sagaut P 2009 J. Comput. Phys.228 1056 [35] Xu H, Malaspinas O and Sagaut P 2012 J. Comput. Phys.231 7335 [36] Xu H and Sagaut P 2011 J. Comput. Phys.230 5353 [37] Chiu P H and Lin Y T 2011 J. Comput. Phys.230 185 [38] Huang R and Wu H 2014 J. Comput. Phys.274 50 [39] Yarin A L 2006 Annu. Rev. Fluid Mech.38 159 [40] Coppola G, Rocco G and de Luca L 2011 Phys. Fluids23 022105 [41] Josserand C and Zaleski S 2003 Phys. Fluids15 1650 [42] Rioboo R, Tropea C and Marengo M 2001 Atomizat. Sprays11 155 [43] Ramaprabhu P, Dimonte G, Young Y N, Calder A C and Fryxell B 2006 Phys. Rev. E74 066308 [44] Goncharov V N 2002 Phys. Rev. Lett.88 134502 [45] Waddell J T, Niederhaus C E and Jacobs J W 2001 Phys. Fluids13 1263 [46] Ding H, Spelt P D M and Shu C 2007 J. Comput. Phys.226 2078 [47] Shao J Y and Shu C 2015 Int. J. Numer. Methods Fluids77 526
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