A 3D Lattice BGK Scheme for Simulation of Thermal Flow in Cubic Cavity

In this paper, a 3D double-population thermal lattice Boltzmann BGK scheme is applied to solve three-dimensional, incompressible thermal fluid flow problem. The simplest lattice BGK D3Q6 model, developed based on passive-scalar approach, is proposed to represent the energy distribution function. While the D3Q19 lattice model is chosen to represent density distribution function in order to calculate the density and velocity fields. The simulation of natural convection in a cubic cavity with Prandtl number 0.71 and Rayleigh number ranging from 10 to 10 are carried out to test the validity of the proposed approach. The flow patterns are observed and the heat transfer rate is estimated in terms of Nusselt number. The dependence of the hear transfer mechanism on the Rayleigh number is shown to agree well with that obtained by the calculations of 3D Navier-Stokes equation. It is observed that the combination of D3Q6 and D3Q19 give excellent numerical stability and accuracy for the simulation at wide range of Rayleigh numbers.