Position of the problem

1)Setting of the parameters

The fluid choosen is water-liquid, it is defined by we  use the Boussinesq-approximation set in the pannel : Define-materials For the pressure, the model used is PRESTO! . If we use the default one, we find that the vertical component of the velocity at the walls is not nul.
with PRESTO!, this problem is resolved Back to the top of the page
2) Generation of the grid

We used Prebfc to generate the mesch.
The grid dimensions are 1cm * 0.5cm . We put 50 cells horizontaly and 25 cells vertically. We used a structured mesch as it is described next.
The boundary conditions are symetry for the vertical sides and walls at different temperatures for the horizontal sides. Back to the top of the page

3) Aim of the study

We have put the lower side at the temperature T2=283k  and the upper at T1=280k. The distance between the two planes is 0.5 cm .we find a Raylleigh number  Ra=3582.5.
Theoritically, with this rayleigh, we can have different nombre of rolls depending of the initial conditions.
Our objectif is to try to find the appropriate initialisation in order to have 1,2,3 and 4 rolls. in each case, we initialise first the temperature. If we don't obtain the
result, we initialise also the velocity. We try in each case to force the motion to go in the wanted direction.
With temperature, we made different zones that create convection which push the fluid to move like the wanted result.
With velocity, we initialise with the result searched . We impose directly the number of rolls using this formula :

Vx=-Vxo.sin(pi.Nb.x /Lx ) cos(pi. y /Ly)
Vy=Vyo.sin(pi. y /Ly ) cos(pi. Nb. x /Lx)

with

Vxo , Vyo : amplitudes
Nb : number of rolls expected
Lx , Ly : Dimensions of the box  in the two dircections

Here is an example of velocity initialisation with four rolls Back to the top of the page