Prediction of natural convection in a square cavity with partially heated from below and symmetrical cooling from sides by the finite difference lattice Boltzmann method

Abstract

In this paper, the lattice Boltzmann method, a numerical tool based on the particle distribution function is used to simulate thermal fluid flow problem. A well-known finite difference technique with third order accuracy in space is combined with the double population thermal lattice Boltzmann model to solve two-dimensional natural convection in a square cavity. The basic idea is to solve the velocity and the temperature field using two different distribution functions. The simulation of localized heated bottom and symmetrical cooling from the sides were carried out in order to validate this approach. The combination of finite difference with double population thermal lattice Boltzmann model is found to be an efficient and stable numerical approach for low and moderate Rayleigh number calculations.