A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity

In this paper, a double-population thermal Lattice Boltzmann method has been proposed to solve the problem of the heated cavity with imposed temperatures. A Taylor series expansion – and least square – based Lattice Boltzamnn method (TLLBM) has been implemented in order to use a non-uniform mesh. This allowed to investigate, at reasonable computational cost, the laminar and transitional flow fields (103 ⩽ Ra ⩽ 108). The numerical results, concerning the heat and mass transfers in the cases tested, are in good agreement with those from the literature. This enables the use of such method for predicting thermal flows of engineering interest.