An explicit lattice Boltzmann method (LBM) is developed in this paper to simulate flows in an arbitrary geometry. The method is based on the standard LBM, Taylor-series expansion, and the least-squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Theoretical analysis for the one-dimensional (1D) case showed that the version of the LBM could recover the Navier-Stokes equations with second order accuracy. A generalized hydrodynamic analysis is conducted to study the wave-number dependence of shear viscosity for the method. Numerical simulations of the 2D lid-driven flow in a square cavity and a polar cavity flow as well as the “no flow” simulation in a square cavity have been carried out. Favorable results were obtained and compared well with available data in the literature, indicating that the present method has good prospects in practical applications.

• Received 1 August 2001

DOI:https://doi.org/10.1103/PhysRevE.65.036708