Lattice Boltzmann simulations of thermal convective flows in two dimensions

In this paper we study the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model for incompressible thermo-hydrodynamics with the Boussinesq approximation. We use the MRT thermal LBE (TLBE) to simulate the following two flows in two dimensions: the square cavity with differentially heated vertical walls and the Rayleigh–Bénard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra=103–106Ra=103–106, and the Prandtl number Pr=0.71Pr=0.71; and for the Rayleigh–Bénard convection in a rectangle, Ra=2⋅103Ra=2⋅103, 104104 and 5⋅1045⋅104, and Pr=0.71Pr=0.71 and 7.0.