Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers

The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal con- vective ows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimension- less ow parameters are the following: the Prandtl number Pr = 0:71 and the Rayleigh number Ra = 106, 107, and 108. The D2Q9+D2Q5 MRT-TLBE is shown to be second-order accurate and to be capable of yielding results of benchmark quality, including various Nusselt numbers and local hydrody- namic intensities. The results obtained by using the MRT-TLBE agree well with existing benchmark data obtained by other methods.