A mass-conserved multiphase lattice Boltzmann method based on high-order difference

doi:10.1088/1674-1056/ab6834

中国物理B ›› 2020, Vol. 29 ›› Issue (3): 34701-034701.doi: 10.1088/1674-1056/ab6834

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

Zhang-Rong Qin(覃章荣), Yan-Yan Chen(陈燕雁), Feng-Ru Ling(凌风如), Ling-Juan Meng(孟令娟), Chao-Ying Zhang(张超英)

Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing, Guangxi Normal University, Guilin 541004, China

收稿日期:2019-06-25 修回日期:2019-10-31 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: Chao-Ying Zhang E-mail:zhangcy@gxnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11862003 and 81860635), the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2017GXNSFDA198038), the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFAA281302), the Project for Promotion of Young and Middle-aged Teachers' Basic Scientific Research Ability in Guangxi Universities, China (Grant No. 2019KY0084), and the “Bagui Scholar” Teams for Innovation and Research Project of Guangxi Zhuang Autonomous Region, China, and the Graduate Innovation Program of Guangxi Normal University, China (Grant No. JXYJSKT-2019-007).

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

Zhang-Rong Qin(覃章荣), Yan-Yan Chen(陈燕雁), Feng-Ru Ling(凌风如), Ling-Juan Meng(孟令娟), Chao-Ying Zhang(张超英)

Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing, Guangxi Normal University, Guilin 541004, China

Received:2019-06-25 Revised:2019-10-31 Online:2020-03-05 Published:2020-03-05
Contact: Chao-Ying Zhang E-mail:zhangcy@gxnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11862003 and 81860635), the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2017GXNSFDA198038), the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFAA281302), the Project for Promotion of Young and Middle-aged Teachers' Basic Scientific Research Ability in Guangxi Universities, China (Grant No. 2019KY0084), and the “Bagui Scholar” Teams for Innovation and Research Project of Guangxi Zhuang Autonomous Region, China, and the Graduate Innovation Program of Guangxi Normal University, China (Grant No. JXYJSKT-2019-007).

摘要/Abstract

摘要： The Z-S-C multiphase lattice Boltzmann model [Zheng, Shu, and Chew (ZSC), J. Comput. Phys. 218, 353 (2006)] is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out, including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

关键词: lattice Boltzmann method, high-order difference, mass conservation, large density ratio

Abstract: The Z-S-C multiphase lattice Boltzmann model [Zheng, Shu, and Chew (ZSC), J. Comput. Phys. 218, 353 (2006)] is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out, including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Key words: lattice Boltzmann method, high-order difference, mass conservation, large density ratio

中图分类号: (Computational methods in fluid dynamics)

47.11.-j

05.50.+q (Lattice theory and statistics) 47.61.Jd (Multiphase flows) 02.70.Bf (Finite-difference methods)

覃章荣, 陈燕雁, 凌风如, 孟令娟, 张超英. A mass-conserved multiphase lattice Boltzmann method based on high-order difference[J]. 中国物理B, 2020, 29(3): 34701-034701.

Zhang-Rong Qin(覃章荣), Yan-Yan Chen(陈燕雁), Feng-Ru Ling(凌风如), Ling-Juan Meng(孟令娟), Chao-Ying Zhang(张超英). A mass-conserved multiphase lattice Boltzmann method based on high-order difference[J]. Chin. Phys. B, 2020, 29(3): 34701-034701.

参考文献 41

[1]	Ye H F, Kuang B and Yang Y H 2019 Chin. Phys. B 28 014701 doi: 10.1088/1674-1056/28/1/014701
[2]	Wen B H, Chen Y Y, Zhang R L, Zhang C Y and Fang H P 2013 Chin. Phy. Lett. 30 064701 doi: 10.1088/0256-307X/30/6/064701
[3]	Hu M D, Zhang Q Y, Sun D K and Zhu M F 2019 Acta Phys. Sin. 68 030501 (in Chinese)
[4]	Gunstensen A K, Rothman D H, Zaleski S and Zanetti G 1991 Phys. Rev. A 43 4320 doi: 10.1103/PhysRevA.43.4320
[5]	Shan X and Chen H 1993 Phys. Rev. E 47 1815 doi: 10.1103/PhysRevE.47.1815
[6]	Shan X and Chen H 1994 Phys. Rev. E 49 2941 doi: 10.1103/PhysRevE.49.2941
[7]	Swift M R, Osborn W R and Yeomans J M 1995 Phys. Rev. Lett. 75 830 doi: 10.1103/PhysRevLett.75.830
[8]	He X Y, Chen S Y and Zhang R Y 1999 J. Comput. Phys. 152 642 doi: 10.1006/jcph.1999.6257
[9]	Wang Y, Shu C, Shao J Y, Wu J and Niu X D 2015 J. Comput. Phys. 290 336 doi: 10.1016/j.jcp.2015.03.005
[10]	Inamuro T, Konishi N and Ogino F 2000 Comput. Phys. Commun. 129 32 doi: 10.1016/S0010-4655(00)00090-4
[11]	Lee T and Lin C L 2005 J. Comput. Phys. 206 16 doi: 10.1016/j.jcp.2004.12.001
[12]	Zheng H W, Shu C and Chew Y T 2006 J. Comput. Phys. 218 353 doi: 10.1016/j.jcp.2006.02.015
[13]	Huang H, Zheng H, Lu X and Shu C 2010 Int. J. Numer. Meth. Fluids 63 119
[14]	Cheng M, Hua J and Lou J 2010 Comput. Fluids 39 260 doi: 10.1016/j.compfluid.2009.09.003
[15]	He B, Yang S C, Qin Z R, Wen B H and Zhang C Y 2017 Sci. Rep. 7 11841 doi: 10.1038/s41598-017-12189-7
[16]	Van Der Sman R G M and Van Der Graaf S 2008 Comput. Phys. Commun. 178 492 doi: 10.1016/j.cpc.2007.11.009
[17]	Zheng L, Lee T, Guo Z and David R 2014 Phys. Rev. E 89 033302 doi: 10.1103/PhysRevE.89.033302
[18]	Son G 2001 Num. Heat Tr. B-Fund. 39 509 doi: 10.1080/104077901750188868
[19]	Chao J, Mei R, Singh R and Wei S 2011 J. Num. Meth. Fluid 66 622 doi: 10.1002/fld.2276
[20]	Huang H, Huang J and Lu X 2014 J. Comput. Phys. 269 386 doi: 10.1016/j.jcp.2014.03.028
[21]	Niu X D, Li Y and Ma Y R 2018 Phys. Fluids 30 013302 doi: 10.1063/1.5004724
[22]	Shao J Y, Shu C, Huang H B and Chew Y T 2014 Phys. Rev. E 89 033309 doi: 10.1103/PhysRevE.89.033309
[23]	Kupershtokh A L, Medvedev D A and Karpov D I 2009 Comput. Math. Appl. 58 965 doi: 10.1016/j.camwa.2009.02.024
[24]	Jacqmin D 1999 J. Comput. Phys. 155 96 doi: 10.1006/jcph.1999.6332
[25]	Kendon V M, Cates M E, Desplat J, Pagonabarraga I and Bladon P 2001 J. Fluid Mech. 440 147 doi: 10.1017/S0022112001004682
[26]	Takada N, Misawa M, Tomiyama A and Hosokawa S 2001 J. Nucl. Sci. Technol. 38 330 doi: 10.1080/18811248.2001.9715037
[27]	Jamet D, Torres D and Brackbill J U 2002 J. Comput. Phys. 182 262 doi: 10.1006/jcph.2002.7165
[28]	Rowlinson J S and Widom B 1989 Molecular Theory of Capillarity (Oxfordshire: Clarendon Press) p. 356
[29]	Jamet D, Lebaigue O, Coutris N and Delhaye J M 2001 J. Comput. Phys. 169 624 doi: 10.1006/jcph.2000.6692
[30]	Lamura A and Succi S 2003 Int. J. Mod. Phys. B 17 145 doi: 10.1142/S0217979203017230
[31]	Wang Y 2011 Mathematics in Practice and Theory 41 16 (in Chinese)
[32]	Wang Y 2009 J. Tianjin Univ. Technol. 25 37 (in Chinese)
[33]	Ding H, Spelt P D M and Shu C 2007 J. Comput. Phys. 226 2078 doi: 10.1016/j.jcp.2007.06.028
[34]	Batchelor G K 1967 An introduction to fluid dynamics (London: Cambridge University Press) p. 658
[35]	Premnath K N and Abraham J 2007 J. Comput. Phys. 224 539 doi: 10.1016/j.jcp.2006.10.023
[36]	Bhaga D and Weber M E 1981 J. Fluid Mech. 105 61 doi: 10.1017/S002211208100311X
[37]	Clift R, Grace J R and Weber M E 2005 Bubbles, drops, and particles (New York: Dover Publications) p. 381
[38]	Hua J, Stene J F and Ping L 2008 J. Comput. Phys. 227 3358 doi: 10.1016/j.jcp.2007.12.002
[39]	Ren F, Song B and Sukop M C 2016 Ad. Water Resour. 97 100 doi: 10.1016/j.advwatres.2016.08.012
[40]	Li X, Gao D Y and Hou B L 2019 Chem. Eng. Sci. 193 76 doi: 10.1016/j.ces.2018.08.061
[41]	Hua J and Lou J 2007 J. Comput. Phys. 222 769 doi: 10.1016/j.jcp.2006.08.008

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

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