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 334^{th}
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.