Solução numérica de problemas darcianos convectivos mão-lineares através do método dos elementos de contorno

Abstract

In this study are presented the mathematical model and numerical solution for problems of convective flow in porous media, i.e. diffusion and advection phenomena dealt with together.The momentum equation is transformed in a Poisson equationdue to Darcian hypothesis, in which the velocity and pressure fields are calculated in order to define the diffusive-advective model. The problem, therefore, results non-linear due to dependence on pressures and velocities in the temperature and flow fields. The Rayleigh number appears as a governing factor of the advective transport participation in the model, and it mathematically comprises a source term or domain action in the Poisson equation. These coupled equations are solved through the Boundary Element Method (BEM) using an iterative procedure, in which the Dual Reciprocity Formulation is used in both equations —Poisson and Advection/Diffusion —in order to deal with the source terms. Numerical experiments in two uncoupled test-problems were implemented so as to test capacity and accuracy of BEM. Later, a more elaborate example was solved, in which several factors such as mesh refinement and Rayleigh number alteration were tested for assessing method sensitivity in this class of nonlinear coupled problems.