Simplified mesoscale lattice boltzmann numerical model for prediction of natural convection in a square enclosure filled with homogeneous porous media

Abstract

The lattice Boltzmann method (LBM) is applied to a generalised isotropic porous media model in a square geometry by introducing a force term to the evolution equation and a porosity to the density equilibrium distribution function. The temperature field is obtained by simulating a simplified thermal model which uses less velocity directions for the equilibrium distribution function and neglects the compression work done by the pressure and the viscous heat dissipation. The reliability of this model for natural convective heat transfer simulation is studied by comparing with results from previous simulations at a porosity value, e = 0.9999. The model is then used for simulation at e = 0.4, 0.6 and 0.9 at three different Rayleigh numbers. Comparison of solutions with previous works confirms the applicability of the present approach.