| The lattice Boltzmann method is a new numerical technique based on kinetictheory to simulate fluid flows in recent years. Compared with other computationalfluid dynamics approaches, the method is simple, intrinsically parallel, and easy toincorporate complex boundary conditions. Although, there has a progress in employingthe lattice Boltzmann equation for fluid dynamics and modeling complex physics influids recently, there some problems need to be solved, such as the non-uniform latticeand curve boundary conditions are very difficult for the standard lattice Boltzmannmethod dealing with. The computational model, boundary conditions and non-uniform lattice methodare studied in detail in the paper. For computational model, an implicit scheme ispresented. A parameter factor is introduced into the lattice Boltzmann equation and theparameter factor is independent with the relaxation time factor. For boundaryconditions, a new scheme is developed in which the macroscopic quantities on thecomputational boundary nodes can be obtained from the macroscopic quantities on thephysical boundary nodes. For non-uniform lattice model, a nested boundary conditionscheme is proposed. In the scheme, the computational domain is divided into someregular sub-domains with the nested boundaries. The distribution function can becomputed by uniform lattice Boltzmann method within sub-domains and bynon-equilibrium extrapolation scheme on the boundaries. Three cases of flow past square cylinders are investigated in the paper. For case 1,the square cylinder is located at the center of the channel, the karman vortex issuccessfully simulated and the Strouhal numbers at different Reynolds numbers aregiven; For case 2, the square cylinder is located at a wall of flow field, the recirculationlengths behind the square cylinder at different Reynolds numbers are considered; Forcase 3, two square cylinders arranged side by side in the center of the channel, the flowfeatures at different spacing ratios are studied.
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