中国物理B ›› 2002, Vol. 11 ›› Issue (4): 366-374.doi: 10.1088/1009-1963/11/4/310

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Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method

施保昌1, 郭照立2, 郑楚光2   

  1. (1)Department of Mathematics, Huazhong University of Science and Shenyang 110023, China; (2)National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2001-09-01 修回日期:2001-10-12 出版日期:2002-04-13 发布日期:2005-06-13
  • 基金资助:
    Project supported by the Special Funds for Major State Basic Research Programmes (Grant No G1999022207) and by the National Natural Science Foundation of China (Grant No 6073044).

Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method

Guo Zhao-Li (郭照立)a, Zheng Chu-Guang (郑楚光)a, Shi Bao-Chang (施保昌)b   

  1. a National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China; b Department of Mathematics, Huazhong University of Science and Shenyang 110023, China
  • Received:2001-09-01 Revised:2001-10-12 Online:2002-04-13 Published:2005-06-13
  • Supported by:
    Project supported by the Special Funds for Major State Basic Research Programmes (Grant No G1999022207) and by the National Natural Science Foundation of China (Grant No 6073044).

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摘要： In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).

Abstract: In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).

Key words: Lattice Boltzmann method, Boundary conditions

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

  • 47.10.-g
05.50.+q (Lattice theory and statistics) 02.60.Ed (Interpolation; curve fitting)