Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
1997/12/01 by Xiaoyi He, Li-Shi Luo, Li‐Shi Luo · 39 citations
Engineering · #Aerodynamics and Fluid Dynamics Research #Aerosol Filtration and Electrostatic Precipitation #Lattice Boltzmann Simulation Studies
paper · doi:10.1103/physreve.56.6811
openalex publication_date 1997/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract
In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.
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