Conclusion.
 

According to us, the first conclusion that we could learn from this hands-on is that it is not obvious to determine precisely a critical number (i.e. associated to a transition of the flow) with an industrial code: there are lots of models (numerical schemes, physical models, ...), and there are also several techniques to get a value from the same set of datas.

What we have retained from all these computations may be summed up this way:

The mesh influence is very important. Typically, when the number N of cells in the mesh increases, the result (velocity, temperature,...) at a given point tends to a limit value, but the number of iterations required for the achievement of the convergence increase like N too. Moreover, the computation time incresases like (Number of cell)2x(Number of iterations).
Finally, the CPU time to observe the convergence on a N-cells mesh increases like N3, for a given e=(Ra-Rac)/Rac.
This is a very fast evolution law and it seems to us very difficult to achieve an accurate determination of Rac, because the number of iterations required to converge increases a lot when e tends to zero.

We can sum this up into a single formula:

TCPU ~ N3/e.


Concerning the different methods we proposed, they all have different advantages and drawbacks. We recall them to the mind of the reader below.


Finally, the best method to obtain an accurate value of Rac in a short amount of time may be to use this last method on a small mesh, and then to interpolate the "real" result by scaling the values we obtained thanks to a mesh-correction factor, which could be found with a single computation on the coarse grid.