There is a lot of studies done around the Rayleigh Benard instabilities. Its complexity make it difficult to understand the hole phenomena by solving numerically N&S equations. The experimental ways are useful. But numerical ways allowed us to show the existence of hydrodynamics instability. And to study the performance of computational methods.

We noticed that a physical knowledge is very important for validating the method and interpreting the results.

Using Phoenics help us to understand the structure of a computational code and the difficulties related to its exploitation. This code was especially useful when we were changing the grid. Another code has been used in this BES : Fluent. For this one we focused on the numerical aspects : convergence time, precision,...etc.

Note that there exist many other codes, witch can be more adapted to some specific problems but our purpose here was to use a didactic, and general ones.

We keep from this study a general idea of how codes are handled. We shall keep in mind too, both the possibilities that a code can offer us to abort such problems, without forgetting that some limits may exist.