中国物理B ›› 2008, Vol. 17 ›› Issue (1): 238-248.doi: 10.1088/1674-1056/17/1/042

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Lattice Boltzmann method with the cell-population equilibrium

程冰1, 周晓阳2, 施保昌2   

  1. (1)Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China\;Department of Science Institute, Qingdao Agricultural University, Qingdao 266109, China\; (2)Huazhong University of Science and Technology, Wuhan 430074, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70271069 and 60773195).

Lattice Boltzmann method with the cell-population equilibrium

Zhou Xiao-Yang(周晓阳)a)†,Cheng Bing(程冰)a)b), and Shi Bao-Chang(施保昌)a)   

  1. a Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China; b Department of Science Institute, Qingdao Agricultural University, Qingdao 266109, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70271069 and 60773195).

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摘要： The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman--Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.

关键词: lattice Boltzmann method, non-negative equilibrium, cell approximation scheme, dam-break

Abstract: The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman--Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.

Key words: lattice Boltzmann method, non-negative equilibrium, cell approximation scheme, dam-break

中图分类号:  (General theory in fluid dynamics)

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