Boundary domain integral method for the study of double diffusive natural convection in porous media

The main purpose of this paper is to present a boundary domain integral method (BDIM) for the solution of natural convection in porous media driven by combining thermal and solutal buoyancy forces. The Brinkman extension of the classical Darcy equation is used for the momentum conservation equation. The numerical scheme was tested on a natural convection problem within a square porous cavity, where different temperature and concentration values are applied on the vertical walls, while the horizontal walls are adiabatic and impermeable. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared with published work. There is a good agreement between those results obtained using the presented numerical scheme and reported studies using other numerical methods.