We compared the results obtained by a steady simulation and the results obtained after a long simulated time by an unsteady simulation. The simulation time is the the time needed by the flow to stabilize at the permanent state. This time is evaluated by that is detailed below. with Prandt number  and Kappa expression: and  with To be sure that the steady state is reached, we calculated during a longer time than the time predicted by this method.

In the case we studied, we have :

• =0.2 K
• K=1.43 10-7
• Pr= 6.99
• Ra=2500
• =250 s The unsteady calculation was conducted until simulated time raise up to 350 seconds. The theorical time for steady state to establish is 250 seconds.
The steady calculation was conducted until the 334th iteration, it has converged the next criterions.
Continuity : 10-3
X velocity : 10-3
Y velocity : 10-3
Energy : 10-6

We can see on the chart that the shape of the velocity amplitude is very similar in the two case. The difference between those two case is the value of velocity amplitude. There is no velocity presented here because the two are very similar and so have little interest to show the difference between this two different way of simulating.
We think that the unsteady calculation gives the more realistic results because the solution is converged at each time step.