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A method simplifying the exteal force term for the Boltzmann equation is proposed, using the Chapman-Enskog asymptotic expansion technique. The relationship between the perturbation strength parameter and the Grashof number is presented. A heat flux boundary condition for the temperature field simulation is developed according to the transforming relations between the cold and hot particles on the boundary wall. The effects of buoyant force and the heat flux boundary condition are implemented with the two-particle systems of D2Q9 and D3Q 15,and the numerical results agree well with the experimental result of silicone oil.