Boundary conditions for the lattice Boltzmann method

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Abstract
When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints 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 (inward-pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3-D body-centered-cubic lattices are presented for Poiseuille flow, porous-plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two-dimensional (2-D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3-D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3-D low-Reynolds-number flow.