Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity

Abstract

In this article, a comparative analysis of thermal models in the lattice Boltzmann method for the simulation of natural convection in a square cavity is presented. A hybrid method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum equations are solved by the lattice Boltzmann method (LBM), is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred-correction method to ensure accuracy of solutions. The resulting algebraic equations are solved by a strongly implicit procedure. The hybrid method is applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the double-population LBM and by the Navier-Stokes equation method. In general, the present hybrid method is as accurate as the Navier-Stokes equation method and the double-population LBM. The hybrid method shows better convergence and stability than the double-population LBM. These observations indicate that this hybrid method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problems involving complex geometries.