Discretizations for the Incompressible Navier--Stokes Equations Based on the Lattice Boltzmann Method

Authors:
Michael Junk;Axel Klar
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2000

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Abstract

A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier--Stokes equation, which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.