Grid independence

Grid independence was tested by obtaining solutions with the 16$\times$16 mesh of 8-noded quadrilateral elements shown in figure 5.3 and on one of half the resolution: 8$\times$8 elements, with the same stretching factor, $s=2$. The independence criteria chosen were those related to the mass transfer rate: the vertical integrals of the horizontal velocity component. Three integrals were taken for each grid: on the left wall, the right wall and the entire domain; and the results reported in Table 5.1. The spread of the figures in each set is another measure of the error since by overall conservation of mass and the impermeability of the horizontal boundaries they should be equal.

Table 5.1: Tests of grid independence and overall conservation of mass.

CRITERION	88	1616	% CHANGE
$\int_{0}^{\mathcal{A}} u\vert _{x=0} \,\mathrm{d}y$	-0.004232	-0.004251	+0.45
$\int_{0}^{\mathcal{A}} u\vert _{x=1} \,\mathrm{d}y$	-0.004211	-0.004254	+1.02
$\int_{0}^{\mathcal{A}}\!\!\int_{0}^{1} u\,\,\mathrm{d}x\,\,\mathrm{d}y$	-0.004221	-0.004252	+0.73