Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

Journal Article · Mon Dec 01 00:00:00 EST 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.56.6811· OSTI ID:365474

He, Xiaoyi ^[1]

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1. Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

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. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 365474
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 56, Issue 6; Other Information: PBD: Dec 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOLTZMANN EQUATION
LATTICE PARAMETERS
PHASE SPACE
HYDRODYNAMICS