Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (1): 70-78.doi: 10.16088/j.issn.1001-6600.2020.01.009

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A Unified Boundary Condition Based on the Halfway Bounce-back Scheme in Lattice Boltzmann Method

LING Fengru, ZHANG Chaoying, CHEN Yanyan, QIN Zhangrong*   

  1. Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University,Guilin Guangxi 541004, China
  • Received:2018-12-06 Online:2020-01-25 Published:2020-01-15

Abstract: The lattice Boltzmann method can effectively simulate the fluid flow in complex flow fields. However, the reliability of the simulation results strongly depends on the selected boundary treatment methods. Based on the halfway bounce-back scheme, a unified treatment for the curved wall is proposed by improving the curved boundary condition scheme of interpolation. Results from tests are in good agreement with the exact solutions. Compared with several curved boundary condition schemes commonly used in lattice Boltzmann simulation, this method exhibits high accuracy and numerical stability of the complex boundary. The novel method provides a reliable way to solve the common problem of mass leakage in the curved boundary condition, satisfying the mass conservation constraint.

Key words: lattice Boltzmann method, numerical simulation, curved boundary condition, unified boundary condition, halfway bounce-back scheme

CLC Number: 

  • O35
[1] ZARGHAMI A, LOOIJE N, HARRY V D A. Assessment of interaction potential in simulating nonisothermal multiphase systems by means of lattice Boltzmann modeling[J]. Physical Review E, 2015,92(21): 023307. DOI:10.1103/PhysRevE.92.023307.
[2] AIDUN C K, CLAUSEN J R. Lattice-Boltzmann method for complex flows[J]. Annual Review of Fluid Mechanics, 2010, 42(1):439-472. DOI:10.1146/annurev-fluid-121108-145519.
[3] SIDIK N A C, MAMAT R. Recent progress on lattice Boltzmann simulation of nanofluids: A review[J]. International Communications in Heat and Mass Transfer, 2015,66: 11-22. DOI:10.1016/j.icheatmasstransfer.2015.05.010.
[4] ZARGHAMI A, FALCUCCI G, JANNELLI E, et al. Lattice Boltzmann modeling of water entry problems[J]. International Journal of Modern Physics C, 2014,25(12): 1441012. DOI:10.1142/s0129183114410125.
[5] 覃章荣,张超英,丘滨,等.基于CUDA的格子Boltzmann数值模拟加速实现[J].广西师范大学学报(自然科学版),2012,30(4):18-24. DOI:10.16088/j.issn.1001-6600.2012.04.002.
[6] 闻炳海,张超英,刘海燕,等.大血管中血液流动的LBM模拟[J].广西师范大学学报(自然科学版),2008,26(4):22-25. DOI:10.16088/j.issn.1001-6600.2008.04.024.
[7] SUCCI S. The lattice Boltzmann equation: for fluid dynamics and beyond[M]. Oxford: Clarendon Press, 2001:58-60.
[8] WOLFGLADROW D A. Lattice gas cellular automata and lattice Boltzmann models: an introduction[M]. Bremerhaven: Springer, 2005:187-192.
[9] ZIEGLER D P. Boundary conditions for lattice Boltzmann simulations[J]. Journal of Statistical Physics, 1993,71(5): 1171-1177. DOI:10.1007/bf01049965.
[10]LADD A J C, VERBERG R. Lattice-Boltzmann simulations of particle-fluid suspensions[J]. Journal of Statistical Physics, 2001, 104(5):1191-1251. DOI:10.1023/a:1010414013942.
[11]FILIPPOVA O, HÄNEL D. Lattice-Boltzmann simulation of gas-particle flow in filters[J]. Computers and Fluids, 1997, 26(7):697-712. DOI:10.1016/S0045-7930(97)00009-1.
[12]何雅玲, 王勇, 李庆. 格子Boltzmann方法的理论及应用[M]. 北京:科学出版社, 2009:136-141.
[13]MEI R, LUO L S, SHYY W. An accurate curved boundary treatment in the lattice Boltzmann method[J]. Journal of Computational Physics, 1999,155(2): 307-330. DOI:10.1006/jcph.1999.6334.
[14]郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京:科学出版社, 2009:68-72.
[15]BOUZIDI M, FIRDAOUSS M, LALLEMAND P. Momentum transfer of a Boltzmann-lattice fluid with boundaries[J]. Physics of Fluids, 2001, 13(11):3452-3459. DOI:10.1063/1.1399290.
[16]LALLEMAND P, LUO L S. Lattice Boltzmann method for moving boundaries[J]. Journal of Computational Physics, 2003, 184(2):406-421. DOI:10.1016/S0021-9991(02)00022-0.
[17]YU D, REN W, SHYY W. A unified boundary treatment in lattice Boltzmann method[C]// Proceedings of the 41st Aerospace Sciences Meeting and Exhibit.Reston, VA:AIAA, 2003:0953. DOI:10.2514/6.2003-953.
[18]TAO S, HE Q, CHEN B M, et al. One-point second-order curved boundary condition for lattice Boltzmann simulation of suspended particles[J]. Computers and Mathematics with Applications, 2018,76(7):1593-1607. DOI:10.1016/j.camwa.2018.07.013.
[19]MOHAMMADIPOOR O R, NIAZMAND H, MIRBOZORGI S A. Alternative curved-boundary treatment for the lattice Boltzmann method and its application in simulation of flow and potential fields[J]. Physical Review E, 2014, 89(1):013309. DOI:10.1103/PhysRevE.89.013309.
[20]NASH R W, CARVER H B, BERNABEU M O, et al. Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains[J]. Physical Review E, 2014,89(2): 023303. DOI:10.1103/PhysRevE.89.023303.
[21]SANJEEVI S K P, ZARGHAMI A, PADDING J T. Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows[J]. Physical Review E, 2018, 97(4):043305. DOI: 10.1103/PhysRevE.97.043305.
[22]ROHDE M, DERKSEN J J, VAN D A H E A. Volumetric method for calculating the flow around moving objects in lattice-Boltzmann schemes[J]. Physical Review E, 2002, 65(5):056701. DOI:10.1103/PhysRevE.65.056701.
[23]COUPANEC E L, VERSCHAEVE J C G. A mass conserving boundary condition for the lattice Boltzmann method for tangentially moving walls[J]. Mathematics and Computers in Simulation, 2011,81(12): 2632-2645. DOI:10.1016/j.matcom.2011.05.004.
[24]李华兵.晶格玻尔兹曼方法对血液流的初步研究[D]. 上海:复旦大学,2004.
[25]MEI R, SHYY W, YU D, et al. Lattice Boltzmann method for 3-D flows with curved boundary[J]. Journal of Computational Physics, 2000, 161(2):680-699. DOI:10.1006/jcph.2000.6522.
[26]BAO J, YUAN P, SCHAEFER L. A mass conserving boundary condition for the lattice Boltzmann equation method[J]. Journal of Computational Physics, 2008, 227(18):8472-8487. DOI:10.1016/j.jcp.2008.06.003.
[27]LUO L S. Lattice-gas automata and lattice boltzmann equations for two-dimensional hydrodynamics[D]. Atlanta:Georgia Institute of Technology, 1993.
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