Lattice Boltzmann method for incompressible, viscous flow

The theoretical basis of the lattice gas automata and lattice Boltzmann method are derived and discussed in detail. The lattice Boltzmann BGK model (LBGK) is used to solve the viscous flow in two- and three-dimensional cavities driven by moving boundaries. For two-dimensional cavity flow, detailed comparisons between the LBGK and traditional methods are performed for Reynolds numbers up to 7500. Error analysis is extensive and gives a quantitative measure of accuracy over entire parametric range. The convergence rate of the method with solid boundaries is found. Comparisons between the square lattice and the triangular (FHP) lattice are carried out and the acceptable ranges of parameters for these two models are explored. For the three-dimensional cubic cavity, the flow structures are studied in detail for Re = 3,200. The three-dimensional phenomena observed in experimental work are confirmed by the LB simulation. The space and time dependence of vortex structures in the yz- and xz-planes are studied in detail. The correlation of these vortices in the two coordinates planes and the asymmetry phenomenon in the downstream region are found for the first time. Velocity profiles in symmetry plane are compared with 3-D experimental data and 2-D simulation results. The 3-D LB simulations show excellent agreement with experimental work. A new model is proposed for incompressible steady flow. Computational results show that the compressibility error is significantly reduced using this model. A lattice Boltzmann subgrid model for simulating fluid flows at high Reynolds numbers is proposed. The method is applied to a two-dimensional driven cavity flow for Re up to 10{dollar}sp6.{dollar} The instability problem in lattice Boltzmann simulations for high Reynolds numbers is substantially reduced by this model.