Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics1997Vol. 56(6), pp. 6811–6817
Citations Over TimeTop 1% of 1997 papers
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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