Convección natural en medios porosos y libres: simulación numérica

Abstract

Numerical simulations are presented for natural convection in rectangular tilted cavities for a porous medium and for a homogeneous fluid as well. In both cases the mathematical modeling is based on the time dependent Boussinesq approximation which gives an incompressible fluid structure; the momentum equations are given for the Darcy ones in porous medium and for the Navier-Stokes equations in homogeneous fluid. The formulation in stream function and vorticity variables is considered. The numerical simulations are obtained with a simple numerical scheme whose effectiveness relies mainly on a fixed point iterative process to solve the elliptic nonlinear system that is obtained once a convenient second order time discretization is performed on each equation that depends explicitly in time. The iterative process leads to the solution of symmetric linear elliptic equations for which very efficient numerical solvers exist. The parameters involved in the simulations are the Rayleigh number, the aspect ratio, and the inclination angle of the cavity.