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A finite difference interpretation of the lattice Boltzmann method. (English) Zbl 0987.76082
Summary: Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be completely different approach to solve incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, we obtain new starting points for discretization of incompressible Navier-Stokes equations.

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