A 3D lattice bgk scheme for simulation of thermal flow in cubic cavity

Abstract

In this paper, a 3D double-population thermal latticeBoltzmann BGK scheme isapplied to solve three-dimensional, incompressible thermal fluid flow problem. Thesimplest lattice BGK D3Q6 model, developed based on passive-scalar approach, isproposed to represent the energy distributionfunction. While the D3Q19 lattice model ischosen to represent density distribution function in order to calculate the density andvelocity fields. The simulation of natural convection in a cubic cavitywith Prandtl number0.71 and Rayleigh number ranging from 103to 105are carried out to test the validity of theproposed approach. The flow patterns are observedand the heat transfer rate is estimated interms of Nusselt number. The dependence of the hear transfer mechanism on the Rayleighnumber is shown to agree well with that obtained by the calculations of 3D Navier-Stokesequation. It is observed thatthe combination of D3Q6 and D3Q19 give excellent numericalstability and accuracy for the simulation at wide range of Rayleigh numbers.