Parallel solver for unsteady Rayleigh-Bénard problem in limited domains

INTRODUCTION The Rayleigh - B'enard convection is considered a reference problem for the study of the possible routes for the transition from steady flow to fully developed turbulence condition. As matter of fact, Rayleigh - B'enard problem presents such a rich scenario of successive transitions (which can be referred to distinctive mechanisms) that focused the attention of many scientists from the beginning of last century up to now (e.g. [1,2]). The detection of types of instability and the study of its evolution in time are very sensitive to physical as well as numerical perturbations. For this reason a great accuracy has to be achieved in the experimental set up and control, or, if a numerical test is conducted, a particular care has to be paid for reducing the numerical noise and integration errors. The required accuracy has to be obtained by using a large number of mesh points and a very small time step. These two requirements involve an enormous demand in terms of compu