It was decided that we would run our 3D simulations in a parallelepiped of the following dimension: X= 0.2 m, Y=0.5 m, Z=0.01 m

These dimension would enable to develop rotating cells along the Y axis. In order to reduce the time needed for the first simulations, a small mesh was created: Nx=20 cells, Ny=50 cells, Nz=10 cells, that makes a total number of cells N=10 000.

We had many problems to make the runs converge, even at small Rayleigh numbers (around Ra=3000). Here are for example the residuals after 75 iterations. On the "SUN Ultra1" stations each iteration would take around 30 seconds thus we tried to reduce the number of iterations by starting the simulations with better initial conditions (IC). Therefore, we used the "patch" function in fluent to initialise the velocity field.

Here is the function we used and it's visualisation: Vz=0.0003 cos(20*pi*x/0.2). Notice 20 is the number of rolls we wish to have and 0.2 the X dimension of the domain. Here are the residuals after 50 iterations to compare the convergence of patched and not patched IC. Notice that only z-velocity residual is above 1E-3. Despite this problem of convergence, we tryed to visualise 3D instabilities. Here is the result of a simulation at Ra=25000: It is obvious that the rolls are not rectilinear.

This result was encouraging, so we decided to make more runs in a wider range of Ra to determine the range of fully 3D instabilities.

The probem is that we had 3D instabilities nearly at any value of Ra. This is due to the fact that the resolution of the mesh is not high enough in X direction. Indeed, there is only a cell per roll !!!

Consequently, we decided to refine the mesh.