A tridimensional numerical simulation of natural convection laminar flows by the finite element method

The finite element method is used to construct a numerical solution algorithm based on the development of the three-dimensional Navier-Stokes equations and the temperature equation within the framework of the Boussinesq approximation. The method relies on a discretization in time using a linearization of implicit terms. The Stokes algorithm is described for the continuous case, and takes into account the incompressibility constraint through the coupling of pressure and velocity. The method is optimized for the representation of three-dimensional flow through an examination of three methods of streamline integration. The analysis is applied to Rayleigh-Benard instability, first two-dimensionally, where a Fourier analysis of horizontal planes is compared with experimental measurements, and then three-dimensionally, with the simulation of primary and secondary orthogonal axis cross-roll instability.