Effect of a degree of rarefaction on Benard convection

The Benard convection in a rarefied gas was simulated by two dimensional DSMC(Direct Simulation Monte Carlo)method. The simulation was performed by using a virtual gravity with temperature jump effect as an external force acting on each sample molecule and the character and instability of convection was estimated for several Knudsen number Kn, which is a degree of rarefaction of the system, with temperature ratio Th/Tc being varied. It is shown that higher temperature ratio is necessary to form the convection as Kn becomes Iarge and that critical Rayleigh Number Rac may be independent of Kn while the existence of convection strongly depends upon Kn. In addition to critical Rayleigh number, it is predicted for a dilute system that there is a critical value of Knudsen number for the formation of convection.