Lattice Boltzmann equation: Failure or success?

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...

Implicit Schemes for the Lattice Boltzmann Equation

Lattice Boltzmann Equation for Laminar Boundary Flow

A simple method based on the lattice Boltzmann equatio n is presented for the evaluati on of the velocity profile of fluid flows near walls or in the vicinity of the interface between two fluids. The met hod is applied to fluid flow near a wall, to channel flow, and to the transition zone between two fluids flowing parallel to each other in opposite direct ions. The results show good agreement ...

Asymptotic analysis of the lattice Boltzmann equation

In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the Boltzmann equation with the diffusive scaling. The analysis of this model directly leads to the incompressible Navier–Stokes equations, as opposed to the compressible Navier–Stokes equations obtained by the Chapm...

Modeling adsorption with lattice Boltzmann equation

The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, a...