留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

格子Boltzmann方法解扩散方程的复杂边界条件研究

黄俊涛 张力 雍稳安 王沫然

黄俊涛, 张力, 雍稳安, 王沫然. 格子Boltzmann方法解扩散方程的复杂边界条件研究[J]. 应用数学和力学, 2014, 35(3): 305-312. doi: 10.3879/j.issn.1000-0887.2014.03.009
引用本文: 黄俊涛, 张力, 雍稳安, 王沫然. 格子Boltzmann方法解扩散方程的复杂边界条件研究[J]. 应用数学和力学, 2014, 35(3): 305-312. doi: 10.3879/j.issn.1000-0887.2014.03.009
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

格子Boltzmann方法解扩散方程的复杂边界条件研究

doi: 10.3879/j.issn.1000-0887.2014.03.009
基金项目: 国家自然科学基金(51176089);国家重点基础研究发展计划(973计划)(2013CB228301)
详细信息
    作者简介:

    黄俊涛(1991—),男,湖北人,博士生(E-mail: huangjt13@mails.tsinghua.edu.cn)

  • 中图分类号: O242.5; O357.3

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

Funds: The National Natural Science Foundation of China(51176089); The National Basic Research Program of China (973 Program)(2013CB228301)
  • 摘要: 对格子Boltzmann方法求解含第三类边界条件的扩散方程进行了理论和数值研究,构造了一种新的基于bounce-back的边界处理数值格式,用来处理复杂边界问题.借助渐近分析,证明了新方法的数值相容性.用数值算例从不同角度分析了算法的精度和稳定性等,与已有算法相比,新方法在精度、稳定性和效率方面均有较大提高.最后通过一个复杂边界反应扩散的示例演示了新方法应用于复杂多孔介质内多物理化学输运模拟的可行性和有效性.
  • [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
计量
  • 文章访问数:  1530
  • HTML全文浏览量:  89
  • PDF下载量:  1427
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-09-25
  • 修回日期:  2013-12-17
  • 刊出日期:  2014-03-15

目录

    /

    返回文章
    返回