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

Abstract

The two-dimensional form of the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) was recently presented by Shu et al. 8 TLLBM is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least square optimization. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. In this paper, TLLBM is extended to the three-dimensional case. The resultant form keeps the same features as the two-dimensional one. The present form is validated by its application to simulate the three-dimensional lid-driven cavity flow at Re = 100, 400 and 1000. Very good agreement was achieved between the present results and those of Navier-Stokes solvers.