NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅰ)——TWO-DIMENSIONAL CASE

In the paper, a finite differential numerical model is proposed for Benard convection ina non-slippery closed rectangle. By this model, we have discussed the bifurcation character-istics of two-dimensional Benard convection when Prandtl number is 1. The computed re-sults show that if the Rayleigh number Ra≥1.75×10~5, the Benard convection is unsteady andirregular, and that in the transient region of flow pattern, the changing rate of the Nusseltnumber Nu to Ra, dlgNu/dlgRa, is rather smaller than that in the non-transient region.Moreover, in the paper, we have analysed the relation between the shrinking rate of thephase flow and each term in the governing equations of Benard convection. And further,we have developed a new method to calculate the pressure gradient.