BOUNDARY-CONDITIONS FOR THE LATTICE BOLTZMANN METHOD

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.