In this paper, a gas-kinetic Bhatnagar-Gross-Krook (BGK) model is constructed for the Rayleigh-Bénard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed $\mathrm{Pr}=1\mathrm{}$ in the original BGK model [P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954)]. The two-dimensional Rayleigh-Bénard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results.

• Received 28 September 1998

DOI:https://doi.org/10.1103/PhysRevE.60.464