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Physical symmetry and lattice symmetry in the lattice Boltzmann method

Nianzheng Cao1,2, Shiyi Chen1,2, Shi Jin3, and Daniel Martínez1,4

  • 11IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598
  • 22Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
  • 33School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
  • 44Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140

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Phys. Rev. E 55, R21(R) – Published 1 January, 1997

DOI: https://doi.org/10.1103/PhysRevE.55.R21

Abstract

The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme.

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References (17)

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Outline

Information

Phys. Rev. E 55, R21(R)– Published 1 January, 1997
  • Received 29 April 1996

© 1997 American Physical Society

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