ACCURACY OF THE LATTICE BOLTZMANN METHOD FOR SMALL KNUDSEN NUMBER WITH FINITE REYNOLDS-NUMBER

The asymptotic theory proposed by Sone [in Rarefied Gas Dynamics, edit ed by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), p. 737] is a pplied to the investigation of the accuracy of the lattice Boltzmann m ethod (LBM) for small Knudsen number with finite Reynolds number. The S-expansion procedure of the asymptotic theory is applied to LBM with the nine-velocity model and fluid-dynamic type equations are obtained. From the fluid-dynamic type equations it is found that by using the L BM we can obtain the macroscopic flow velocities and the pressure grad ient for incompressible fluid with relative errors of O(epsilon'(2)) w here epsilon' is a modified Knudsen number which is of the same order as the lattice spacing and is related to a dimensionless relaxation ti me. In two problems, the Couette flow with flow injection and suction through porous walls and a three-dimensional flow through a square duc t, the accuracy of LBM is examined for relaxation times between 0.8 an d 1.7 and the validity of the asymptotic theory for LBM is shown. (C) 1997 American Institute of Physics.