New thermal MRT lattice Boltzmann method for simulations of convective flows

The purpose of this paper is to develop a numerical scheme based on the MRT-D2Q9 model for fluid velocity and the MRT-D2Q5 cross model for the temperature to study the natural convection phenomenon in a differentially heated square enclosure containing air. The present work aims to prove the accuracy and the capacity of this model to predict the thermodynamics phenomena. In fact, the main goal consists to demonstrate the efficiency of the double population approach based on new MRT-LBM scheme in the assessment of laminar and transitional flows in natural convection case for different Rayleigh numbers (up to 108). The numerical results of the present work were successfully checked for accuracy and are in satisfactory agreement with those available in literature. The results analysis shows that the present method has proven its ability to handle similar problem. (C) 2015 Published by Elsevier Masson SAS.