Parallel solver for unsteady Rayleigh — bénard problem in limited domains

Publisher Summary The Rayleigh–Benard convection is considered a reference problem for the study of the possible routes for the transition from steady flow to fully developed turbulence condition. The system considered is a three-dimensional box, bounded by rigid and impermeable walls, filled with an incompressible Newtonian fluid and heated from below. Vertical walls are adiabatic, while horizontal walls are isothermal and held at different values of temperature. Domains with small values of aspect ratios have been considered because they are the only domains that allow users to observe interesting bifurcation sequences toward the turbulent regime. The aim of the chapter is to document and examine flow transitions or bifurcations by direct numerical simulations as the control parameter is increased. The third route contains a well-defined regime with three generally incommensurate frequencies. Numerical results and related discussion are presented after a short description of the algorithm and of the parallel performances. All the sequences of instabilities are repeatable, but it is not possible to individuate simple rules for predicting which sequence will occur for given values of the characteristic parameters.