Two-parameter thermal lattice BGK model with a controllable Prandtl number

In this paper, two time relaxation parameters are introduce to a thermal lattice BGK model to make its Prandtl number controllable. The dependency of the Prandtl number on the two parameters is derived. Numerical measurement of the transport coefficients is used to demonstrate the validity of the method. Furthermore, two examples of convective heat transfer are calculated, with one to show the effectiveness, and the other to show the breakdown of the two-parameter formulation under different conditions.