HUANG Jun-tao, ZHANG Li, YONG Wen-an, WANG Mo-ran. On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations[J]. Applied Mathematics and Mechanics, 2014, 35(3): 305-312. doi: 10.3879/j.issn.1000-0887.2014.03.009
Citation: HUANG Jun-tao, ZHANG Li, YONG Wen-an, WANG Mo-ran. On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations[J]. Applied Mathematics and Mechanics, 2014, 35(3): 305-312. doi: 10.3879/j.issn.1000-0887.2014.03.009

On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations

doi: 10.3879/j.issn.1000-0887.2014.03.009
Funds:  The National Natural Science Foundation of China(51176089); The National Basic Research Program of China (973 Program)(2013CB228301)
  • Received Date: 2013-09-25
  • Rev Recd Date: 2013-12-17
  • Publish Date: 2014-03-15
  • The diffusion equation with the third-type boundary condition solved by the lattice Boltzmann method was theoretically and numerically studied. A new numerical algorithm based on the bounce-back method was constructed, to deal with the complex boundary problem. By asymptotic analysis, the compatibility of the numerical method was proved. The accuracy and stability of the algorithm were discussed via several numerical examples. Compared with the previous work, this numerical approach makes a significant improvement in the aspects of accuracy, stability and efficiency. Finally, through the numerical example of a reaction-diffusion problem with complex boundary, feasibility and effectiveness of the presented method are proved in the simulation of the multi-physical and chemical transport process in porous medium.
  • loading
  • [1]
    Li D. Encyclopedia of Microfluidics and Nanofluidics[M]. Springer, 2008.
    [2]
    Squires T M, Quake S R. Microfluidics: fluid physics at the nanoliter scale[J].Reviews of Modern Physics,2005, 〖CX1〗77〖CX〗(3): 977-1026.
    [3]
    Wang M, Kang Q, Viswanathan H, Robbinson B. Modeling of electro-osmosis of dilute electrolyte solutions in silica microporous media[J].Journal of Geophysical Research-Solid Earth,2010,115: B10205.
    [4]
    Fathi E, Akkutlu I Y. Lattice Boltzmann method for simulation of shale gas transport in kerogen[J].SPE Journal,2013,18(1): 27-37.
    [5]
    Nordsveen M, Neic S, Nyborg R, Stangeland A. A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films―part 1: theory and verification[J].Corrosion,2003,59(5): 443-456.
    [6]
    Oliveira R, Melo L, Pinheiro M, Vieira M J. Surface interactions and deposit growth in fouling of heat exchangers[J].Corrosion Reviews,1993,11(1/2): 55-96.
    [7]
    Chen S Y, Doolen G D. Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30: 329-364.
    [8]
    Inamuro T, Yoshino M, Ogino F. Non-slip boundary-condition for lattice Boltzmann simulations[J].Physics of Fluids,1995,7(12): 2928-2930.
    [9]
    ZHANG Ting, SHI Bao-chang, GUO Zhao-li, CHAI Zhen-hua, LU Jian-hua. General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method[J].Physical Review E,2012,85(1): 016701.
    [10]
    Kang Q, Lichtner P C, Zhang D. An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale[J].Water Resources Research,2007,43(12): W12S14.
    [11]
    Ziegler D P. Boundary conditions for lattice Boltzmann simulations[J].Journal of Statistical Physics,1993,71(5/6): 1171-1177.
    [12]
    Gabbanelli S, Drazer G, Koplik J. Lattice Boltzmann method for non-Newtonian (power-law) fluids[J].Physical Review E,2005,72(4): 046312.
    [13]
    PAN Chong-xun, LUO Li-shi, Miller C T. An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers & Fluids,2006,35(8): 898-909.
    [14]
    SHAN Xiao-wen, CHEN Hu-dong. Lattice Boltzmann model for simulating flows with multiple phases and components[J].Physical Review E,1993,47(3): 1815-1819.
    [15]
    Wang M, Chen S. Electroosmosis in homogeneously charged micro- and nanoscale random porous media[J].Journal of Colloid and Interface Science,2007,314(1): 264-273.
    [16]
    WANG Mo-ran. Structure effects on electro-osmosis in microporous media[J].Journal of Heat Transfer,2012,134(5): 051020.
    [17]
    WANG Mo-ran, PAN Ning. Predictions of effective physical properties of complex multiphase materials[J].Material Science and Engineering: R: Reports,2008,63(1): 1-30.
    [18]
    Huang H B, Lu X Y, Sukop M C. Numerical study of lattice Boltzmann methods for a convection-diffusion equation coupled with Navier-Stokes equations[J].Journal of Physics A: Mathematical and Theoretical,2011,44(5): 055001.
    [19]
    Succi S, Smith G, Kaxiras E. Lattice Boltzmann simulation of reactive microflows over catalytic surfaces[J].Journal of Statistical Physics,2002,107(1/2): 343-366.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1656) PDF downloads(1431) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return