Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
- 1 December 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 56 (6) , 6811-6817
- https://doi.org/10.1103/physreve.56.6811
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.Keywords
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