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Discretizations for the incompressible Navier-Stokes equations based on the lattice Boltzmann method. (English) Zbl 0972.76083
A lattice Boltzmann method is constructed in the form of a uniform numerical scheme. In the low Mach number limit, the scheme reduces to a finite difference scheme for incompressible Navier-Stokes equations, which can be considered as projection method with second order spatial discretization on regular grids. The discretization is analyzed, and the method is compared to Chorin’s original spatial discretization. Numerical examples confirm analytical statements.

76M28 Particle methods and lattice-gas methods
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76M20 Finite difference methods applied to problems in fluid mechanics
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