ACCURACY OF THE LATTICE-BOLTZMANN METHOD

The accuracy of the lattice-Boltzmann method (LBM) is moderated by sev eral factors, including Mach number, spatial resolution, boundary cond itions, and the lattice mean free path. Results obtained with 3D latti ces suggest that the accuracy of certain two-dimensional (2D) flows, s uch as Poiseuille and Couette how, persist even when the mean free pat h between collisions is large, but that of the 3D duct flow deteriorat es markedly when the mean free path exceeds the lattice spacing. Accur acy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicabilit y of LBM to 3D low-Reynolds-number flow. The influence of boundary rep resentations on LBM accuracy is captured by the proposed index, when t he accuracy of the prescribed boundary conditions is consistent with t hat of LBM.