中国物理B ›› 2001, Vol. 10 ›› Issue (7): 587-593.doi: 10.1088/1009-1963/10/7/301

• •    下一篇

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

冯士德2, Tsutahara Michihisa1, 季仲贞2   

  1. (1)Division of Industrial Science, Graduate School of Technology and Science, Kobe University, Japan; (2)Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 收稿日期:2001-01-16 修回日期:2001-01-13 出版日期:2001-07-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 49823002, 7-200053, 4-200060 and 8-1502) and by the National Key Planning Development Project for Basic Research (Grant No. G1999032801).

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

Feng Shi-de (冯士德)a, Tsutahara Michihisab, Ji Zhong-zhen (季仲贞)a   

  1. a Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China; b Division of Industrial Science, Graduate School of Technology and Science, Kobe University, Japan
  • Received:2001-01-16 Revised:2001-01-13 Online:2001-07-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 49823002, 7-200053, 4-200060 and 8-1502) and by the National Key Planning Development Project for Basic Research (Grant No. G1999032801).

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摘要： A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity uα. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.

Abstract: A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity $u_\alpha$. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.

Key words: lattice Boltzmann equation model, hydrodynamic equations, thermal convection

中图分类号:  (Transport processes)

  • 05.60.-k
05.50.+q (Lattice theory and statistics) 05.20.Jj (Statistical mechanics of classical fluids) 47.20.Bp (Buoyancy-driven instabilities (e.g., Rayleigh-Benard)) 47.27.te (Turbulent convective heat transfer)