Thermal lattice-BGK model based on large-eddy simulation of turbulent natural convection due to internal heat generation

To simulate turbulent convection at high Rayleigh number (Ra), we propose a new thermal lattice-BGK (LBGK) model based on large eddy simulation (LES). Two-dimensional numerical simulations of natural convection with internal heat generation in a square cavity were performed at Ra from 106 to 1013 with Prandtl numbers (Pr) at 0.25 and 0.60. Simulation results indicate that our model is fit to simulate high Ra flow for its better numerical stability. At Ra = 1013, a global turbulent has occurred. With a further increase in Ra, the flow will arrive in a fully turbulence regime. The Nusselt–Rayleigh relationship is also discussed.