A tridimensional numerical simulation of natural convection laminar flows by the finite element method
Abstract
The finite element method is used to construct a numerical solution algorithm based on the development of the threedimensional NavierStokes 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 threedimensional flow through an examination of three methods of streamline integration. The analysis is applied to RayleighBenard instability, first twodimensionally, where a Fourier analysis of horizontal planes is compared with experimental measurements, and then threedimensionally, with the simulation of primary and secondary orthogonal axis crossroll instability.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT........35C
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Free Convection;
 Laminar Flow;
 Three Dimensional Flow;
 Boussinesq Approximation;
 Fourier Analysis;
 NavierStokes Equation;
 Numerical Integration;
 Perturbation Theory;
 RayleighBenard Convection;
 Two Dimensional Flow;
 Variational Principles;
 Vortices;
 Fluid Mechanics and Heat Transfer