Taylor-series expansion and least-squares-based lattice Boltzmann method: Two-dimensional formulation and its applications

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.