Numerical analysis of incompressible flows by the lattice boltzmann method

Abstract

A lattice Boltzmann method for one-phase incompressible flows is proposed. The conventional lattice Boltzmann equation leads to the compressible Navier-Stokes equations through the ChapmanEnskog expansion. The compressible error is eliminated by applying the Fractional Step method to the conventional LB method. Two particle velocity distribution functions are used in this method : one calculates the momentum, and the other does the pressure in numerical computations. This method is able to compute the fluid flows as the density is constant, that is, the sound velocity is infinity. This method is validated by simulations of the Taylor vortex flow, of the Poiseuille flow, and of the cavity flow. The proposed model eliminates the pressure oscillation observed in the simulations of the Taylor vortex flow. The simulations show that the both errors of the continuity equation and of the fluid velocity reduce to about one-tenth. The numerical results of the proposed model are more accurate than those of the conventional LB method.