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Lattice Boltzmann model for the incompressible Navier-Stokes equation. (English) Zbl 0939.82042
Summary: In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of \(o(M^2)\), where \(M\) is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure \(p\) instead of the mass density \(\rho\) is the independent dynamic variable. The incompressible Navier-Stokes equations are derived from the incompressible LB model via Chapman-Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.

MSC:
76M28 Particle methods and lattice-gas methods
76D05 Navier-Stokes equations for incompressible viscous fluids
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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