When the Lattice Boltzmann Method (LBM) is used for simulating continu
um fluid flow, the discrete mass distribution must satisfy imposed con
straints for density and momentum along the boundaries of the lattice.
These constraints uniquely determine the three-dimensional (3-D) mass
distribution for boundary nodes only when the number of external (inw
ard-pointing) lattice links does not exceed four. We propose supplemen
tary rules for computing the boundary distribution where the number of
external links does exceed four, which is the case for all except sim
ple rectangular lattices. Results obtained with 3-D body-centered-cubi
c lattices are presented for Poiseuille flow, porous-plate Couette flo
w, pipe flow, and rectangular duct flow. The accuracy of the two-dimen
sional (2-D) Poiseuille and Couette flaws persists even when the mean
free path between collisions is large, but that of the 3-D duct flow d
eteriorates markedly when the mean free path exceeds the lattice spaci
ng. Accuracy in general decreases with Knudsen number and Mach number,
and the product of these two quantities is a useful index for the app
licability of LBM to 3-D low-Reynolds-number flow. (C) 1996 American I
nstitute of Physics.