## 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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