Derivation of lattice Boltzmann equation via analytical characteristic integral

A priori derivation of the lattice Boltzmann equation

The lattice Boltzmann equation ~LBE! is directly derived from the Boltzmann equation by discretization in both time and phase space. A procedure to systematically derive discrete velocity models is presented. A LBE algorithm with arbitrary mesh grids is proposed and a numerical simulation of the backward-facing step is conducted. The numerical result agrees well with experimental and previous n...

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

Xiaoyi He1,2,* and Li-Shi Luo Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Complex Systems Group T-13, MS-B213, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ICASE, MS 403, NASA Langley Research Center, 6 North Dryden Street, Building 1298, Hampton, Virginia 23681-0001 ~Received 29 April 1997; revised ma...

Alternative and Explicit Derivation of the Lattice Boltzmann Equation for the Unsteady Incompressible Navier-Stokes Equation

Derivation of the Lattice Vehicular Model from the Boltzmann Transport Equation

In this paper, the lattice vehicular model, which is in the form 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. A 3-bit approximation, which describe uncongested traffic flow, for the discretization of the Boltzmann equation in both time and phase space is di...

On the derivation of a linear Boltzmann equation from a periodic lattice gas

describes the evolution of a density of particles in a medium in which the particles don’t interact among themselves. The motion of each particle is described by a jump process: The speed of a particle is constant (equal to one), and also the direction is constant in exponentially distributed time intervals. At the end of such an interval, the direction jumps according to a law that corresponds...