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A thermal lattice Bhatnagar-Gross-Krook (LBGK) model with a robust boundary scheme is developed for Boussinesq incompressible fluids. In the model the velocity and temperature fields are solved by two independent LBGK equations which are combined into a coupled equation for the whole system. The two-dimensional natural convection flow of air in a differentially heated cavity of an aspect ratio of four is simulated for the Rayleigh number up to 1010. The numerical results are found to be in good agreement with those of previous studies.