In this case, we wanted to see the behavior of the calculation faced
to the first problem we have treated (Ra = 25000) but in three dimensions.
Conditions of the Calculation
The domain is 3 cm length, 2 cm width and 1 cm height.
The grid is composed of 24000 squared cells (30x40x20). That is to say half time the proportion used in the 2D case. The fact of not keeping the same number of cells for each segment is due, of course, to the calculation time which is considerably increased.
The boundaries conditions are:
 symmetry on the vertical boundaries
 Temperature given on the walls
All others parameters or way of calculation are exactly the same than in the 2D case.
In the 3D case, we obtain an extrapolation of the 2D results. That is to say that we find the same kind of profiles for temperature (mushroom) and velocity (rolls) in a cross section.
Nevertheless, with the same conditions (boundary and initial) we find
two rolls in the 3D case, where as in the 2D case,we found three rolls.
Temperature

Velocity

Moreover, the results obtained with the unsteady simulation are not
exactly the same that for the 2D simulation. Indeed, for the temperature
there is not a smooth evolution of the mushroom and also a translation
in the x direction until reaching a steady state.
For the velocity, we can see the development of rolls (axis in the
x direction) that die once the steady state is reached. This shows the
competition between the different possibilities of direction that can be
used by the phenomenon. Finally, this one seems to prefer the longer rolls.