A coupled lattice BGK model for the Boussinesq equations

TLDR

The study develops a thermal lattice BGK model for Boussinesq incompressible fluids. The model couples separate lattice BGK equations for velocity and temperature, and is applied to porous plate flow and two‑dimensional natural convection in a square cavity with Pr = 0.71 across various Rayleigh numbers. Simulations show that the model’s results agree well with analytical solutions and prior studies. © 2002 John Wiley & Sons, Ltd.

Abstract

Abstract In this paper, a thermal lattice BGK model is developed for the Boussinesq incompressible fluids. The basic idea is to solve the velocity field and the temperature field using two independent lattice BGK equations, respectively, and then combine them into one coupled model for the whole system. The porous plate problem and the two‐dimensional natural convection flow in a square cavity with Pr=0.71 and various of Rayleigh numbers are simulated using the model. The numerical results are found to be in good agreement with the analytical solutions or those of previous studies. Copyright © 2002 John Wiley & Sons, Ltd.