As many other persons, we
tested the influence of the mesh, specially on the critical Rayleigh number.
Our results lead to the same conclusions. Indeed, the more you increase
the number of nodes, the closer to the theorical critical Rayleigh number
you get. However, you always remain under the theorical number, so as you
decrease the number of nodes, you decrease the numerical critical Rayleigh
number.

From a mesh composed of
about 500-1000 nodes, you start to have quite good results. But it is not
very interesting, at least for our utilisation, to have very precise meshes.
Indeed, between two meshes of 2500 nodes and 5000 nodes, the differences
are very small concerning the results but of course, the more precise mesh
takes much more time to converge.

As a remark, we can say that
we tried to get closer and closer from the critical Rayleigh number. Of
course, the calculations take much more time as it is difficult for the
solver to satisfy the convergence criterium.

Here are some visualisations
of simulations made close to the theorical critical Rayleigh number. We
can observe how the instability starts.