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A novel lattice Boltzmann method for dealing with arbitrarily complex fluid-solid boundaries

Shi Dong-Yan Wang Zhi-Kai Zhang A-Man

A novel lattice Boltzmann method for dealing with arbitrarily complex fluid-solid boundaries

Shi Dong-Yan, Wang Zhi-Kai, Zhang A-Man
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  • A suitable arbitrarily complex boundary condition treatment using the lattice Boltzmann sheme is developed in the fluid-solid coupling field. The new method is based on a half-way bounce back model. A virtual boundary layer is built with the fluid-solid coupling, and all the properties used on the virtual boundary are inter-/extrapolated from the surrounding nodes combining with the finite difference method. The improved method ensures that the particles bounce the same location as that of the macro-speed sampling point, and considers the offset effect on the accuracy of the calculated results when the actual physical borders and the grid lines do not coincide. And its scope is extended to any static or mobile, straight or curved boundary. The processing power of the method under the classic conditions, such as the Poiseuille flow, the flow around a circular cylinder, the Couette flow, etc. is studied. Results prove that the theoretically calculated values agree well with the experimental data. Compared with the results published in the literature, this method has a greater precision when the actual physical borders and gridlines do not coincide.
    • Funds: Project supported by the Department Youth Tip-top Talent Support Programme, the Program for New Century Excellent Talents in University of Ministry Education of China(Grant No. NCET100054), and the National Defense Basic Scientific Research program of China(Grant No. B2420133001).
    [1]

    Chen S Y, Doolen G D 1998 Annu RevFluid Mech 30 329

    [2]

    Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese)[郭亚丽, 徐鹤函, 沈胜强, 魏兰2013 物理学报62 144704]

    [3]

    QianY H, Humières D D, Lallemand P 1992 Europhys. Lett. 17 479

    [4]

    He X Y, Luo L S 1997 Phys. Rev. E 56 6811

    [5]

    Mcnamara G R, Zanetti G 1988 Phys. Rev. Lett. 61 2332

    [6]

    Chen S Y, Martinez D, Ren W M 1996 Phys. Fluids 8 2527

    [7]

    Wen B H, Liu H Y, Zhang C Y, Wang Q 2009 Chin. Phys. B 18 4353

    [8]

    Ni B Y, Zhang A M, Wang Q X, Wang B 2012 Acta Mech. Sin. 28 1248

    [9]

    Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮2008 物理学报57 339]

    [10]

    Liu Y L, Zhang A M, Wang S P, Tian S L 2013 Acta Phys. Sin. 62 144703 (in Chinese) [刘云龙, 张阿漫, 王诗平, 田昭丽2013 物理学报62 144703]

    [11]

    Zhang A M, Yao X L 2008 Chin. Phys. B 17 0927

    [12]

    Shan X W, Chen H D 1994 Phys. Rev. E 49 2941

    [13]

    Zhang R Y, He X Y, Chen S Y 2000 Comput. Phys. Commu. 129 121

    [14]

    Xie H Q, Zeng Z, Zhang L Q, Liang G Y, Hiroshi M, Yoshiyuki K 2012 Chin. Phys. B 21 124703

    [15]

    Cheng M, Hua J S, Lou J 2010 Comput. Fluids 39 260

    [16]

    Xu Y, Liu Y, Xia Y, Wu F 2008 Phys. Rev. E 78 046314

    [17]

    Zeng J B, Li L J, Liao Q, Jiang F M 2011 Acta Phys. Sin. 60 066401 (in Chinese)[曾建邦, 李隆键, 廖全, 蒋方明2011 物理学报60 066401]

    [18]

    Shu C, Wu J 2009 Modern Phys. Lett. B 23 261

    [19]

    Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮2013 物理学报 62 084703]

    [20]

    Noble D R, Chen S Y, Georgiadis J G, Buckius R O 1995 Phys. Fluids 7 203

    [21]

    He X Y, Zou Q S, Luo LS, Dembo M 1997 J. Stat. Phys. 87 115

    [22]

    Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1)(Beijin g:Academic Press of China) p62 (in Chinese)[郭照立, 郑楚光2009 格子Boltzmann 方法的原理及应用(第一版) (北京: 科技出版社) 第62 页]

    [23]

    Ladd A J C 1994 J. Fluid Mech. 271 285

    [24]

    Yin X W, Zhang J F 2012 J. Comput. Phys. 231 4295

    [25]

    Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007

    [26]

    Sterling J D, Chen S Y 1996 J. Comput. Phys. 123 196

    [27]

    Bouzidi M, Firdaouss M, Lallemand P 2001 Phys. Fluids 13 3452

    [28]

    Bhatnagar P L, Gross E P, Krook M 1954 Phys. Rev. 94 511

    [29]

    Feng S D, Zhao Y, Gao X L, Ji Z Z 2002 Chinese Phys. Lett. 19 814

    [30]

    Nishida H, Meichin Y 2012 Seventh International Conference on Computational Fluid Dynamics Big Island, Hawaii, July 9-13 1306

    [31]

    He X Y, Doolen G D 1997 Phys. Rev. E 56 434

    [32]

    Braza M, Chassaing P, Minh H H 1986 J. Fluid Mech. 165 79

    [33]

    Tritton D 1959 J. Fluid Mech. 6 547

    [34]

    Liu C, Zheng X, Sung C H 1998 J. Comput. Phys. 139 35

    [35]

    Gerrard J H 1978 Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 288 351

    [36]

    Hammache M, Gharib M 1989 Phys. Fluids A: Fluid Dynamics 1 1611

  • [1]

    Chen S Y, Doolen G D 1998 Annu RevFluid Mech 30 329

    [2]

    Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese)[郭亚丽, 徐鹤函, 沈胜强, 魏兰2013 物理学报62 144704]

    [3]

    QianY H, Humières D D, Lallemand P 1992 Europhys. Lett. 17 479

    [4]

    He X Y, Luo L S 1997 Phys. Rev. E 56 6811

    [5]

    Mcnamara G R, Zanetti G 1988 Phys. Rev. Lett. 61 2332

    [6]

    Chen S Y, Martinez D, Ren W M 1996 Phys. Fluids 8 2527

    [7]

    Wen B H, Liu H Y, Zhang C Y, Wang Q 2009 Chin. Phys. B 18 4353

    [8]

    Ni B Y, Zhang A M, Wang Q X, Wang B 2012 Acta Mech. Sin. 28 1248

    [9]

    Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮2008 物理学报57 339]

    [10]

    Liu Y L, Zhang A M, Wang S P, Tian S L 2013 Acta Phys. Sin. 62 144703 (in Chinese) [刘云龙, 张阿漫, 王诗平, 田昭丽2013 物理学报62 144703]

    [11]

    Zhang A M, Yao X L 2008 Chin. Phys. B 17 0927

    [12]

    Shan X W, Chen H D 1994 Phys. Rev. E 49 2941

    [13]

    Zhang R Y, He X Y, Chen S Y 2000 Comput. Phys. Commu. 129 121

    [14]

    Xie H Q, Zeng Z, Zhang L Q, Liang G Y, Hiroshi M, Yoshiyuki K 2012 Chin. Phys. B 21 124703

    [15]

    Cheng M, Hua J S, Lou J 2010 Comput. Fluids 39 260

    [16]

    Xu Y, Liu Y, Xia Y, Wu F 2008 Phys. Rev. E 78 046314

    [17]

    Zeng J B, Li L J, Liao Q, Jiang F M 2011 Acta Phys. Sin. 60 066401 (in Chinese)[曾建邦, 李隆键, 廖全, 蒋方明2011 物理学报60 066401]

    [18]

    Shu C, Wu J 2009 Modern Phys. Lett. B 23 261

    [19]

    Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮2013 物理学报 62 084703]

    [20]

    Noble D R, Chen S Y, Georgiadis J G, Buckius R O 1995 Phys. Fluids 7 203

    [21]

    He X Y, Zou Q S, Luo LS, Dembo M 1997 J. Stat. Phys. 87 115

    [22]

    Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1)(Beijin g:Academic Press of China) p62 (in Chinese)[郭照立, 郑楚光2009 格子Boltzmann 方法的原理及应用(第一版) (北京: 科技出版社) 第62 页]

    [23]

    Ladd A J C 1994 J. Fluid Mech. 271 285

    [24]

    Yin X W, Zhang J F 2012 J. Comput. Phys. 231 4295

    [25]

    Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007

    [26]

    Sterling J D, Chen S Y 1996 J. Comput. Phys. 123 196

    [27]

    Bouzidi M, Firdaouss M, Lallemand P 2001 Phys. Fluids 13 3452

    [28]

    Bhatnagar P L, Gross E P, Krook M 1954 Phys. Rev. 94 511

    [29]

    Feng S D, Zhao Y, Gao X L, Ji Z Z 2002 Chinese Phys. Lett. 19 814

    [30]

    Nishida H, Meichin Y 2012 Seventh International Conference on Computational Fluid Dynamics Big Island, Hawaii, July 9-13 1306

    [31]

    He X Y, Doolen G D 1997 Phys. Rev. E 56 434

    [32]

    Braza M, Chassaing P, Minh H H 1986 J. Fluid Mech. 165 79

    [33]

    Tritton D 1959 J. Fluid Mech. 6 547

    [34]

    Liu C, Zheng X, Sung C H 1998 J. Comput. Phys. 139 35

    [35]

    Gerrard J H 1978 Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 288 351

    [36]

    Hammache M, Gharib M 1989 Phys. Fluids A: Fluid Dynamics 1 1611

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  • Received Date:  17 October 2013
  • Accepted Date:  06 January 2014
  • Published Online:  05 April 2014

A novel lattice Boltzmann method for dealing with arbitrarily complex fluid-solid boundaries

  • 1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China;
  • 2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Fund Project:  Project supported by the Department Youth Tip-top Talent Support Programme, the Program for New Century Excellent Talents in University of Ministry Education of China(Grant No. NCET100054), and the National Defense Basic Scientific Research program of China(Grant No. B2420133001).

Abstract: A suitable arbitrarily complex boundary condition treatment using the lattice Boltzmann sheme is developed in the fluid-solid coupling field. The new method is based on a half-way bounce back model. A virtual boundary layer is built with the fluid-solid coupling, and all the properties used on the virtual boundary are inter-/extrapolated from the surrounding nodes combining with the finite difference method. The improved method ensures that the particles bounce the same location as that of the macro-speed sampling point, and considers the offset effect on the accuracy of the calculated results when the actual physical borders and the grid lines do not coincide. And its scope is extended to any static or mobile, straight or curved boundary. The processing power of the method under the classic conditions, such as the Poiseuille flow, the flow around a circular cylinder, the Couette flow, etc. is studied. Results prove that the theoretically calculated values agree well with the experimental data. Compared with the results published in the literature, this method has a greater precision when the actual physical borders and gridlines do not coincide.

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