Lattice kinetic scheme for the incompressible viscous thermal flows on arbitrary meshes.

A lattice kinetic scheme was developed for the incompressible viscous thermal flows on arbitrary meshes. The work was based on the lattice kinetic scheme proposed by Inamuro and the technique of Taylor series expansion- and least-square-based lattice Boltzmann method (TLLBM). Compared with the lattice Boltzmann method, the lattice kinetic scheme can save the computer memory since there is no need to store the density distributions. The implementation of the boundary condition is direct and just the same as the convectional Navier-Stokes solvers. By using the idea of TLLBM, the lattice kinetic scheme can be applied on arbitrary meshes, which makes this scheme suitable for practical applications. In order to validate this lattice kinetic scheme used on arbitrary meshes, numerical simulations of the natural convection in a square cavity and the natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder are carried out, and the results are compared very well with available data in the literature.