5.4.2 Dirichlet Type

For Dirichlet boundary conditions one gets

$$\nu_{i} \nu_{C}^{} \nu_{i}^{}$$ = 0 (5.18)

$$\sum_{i}^{} \nu_{i}$$ f_FC = = 0 (5.19)

Here, $\nu_{C}^{}$ is the boundary value of the quantity, which is a solution variable, whereas (5.19) is used as constitutive relation for the actual flow over the boundary F_C.

$\mathbb {T}$_B reads, again for two example grid points i₁ and i₂

tx, y	$\nu_{i_{1}}^{}$	$\nu_{i_{2}}^{}$	FC
$\nu_{i_{1}}^{}$
$\nu_{i_{2}}^{}$
FC	1	1

The rows for $\nu_{i_{1}}^{}$ and $\nu_{i_{2}}^{}$ are zero since substitute equations will directly be provided in the boundary matrix $\mathbb {T}$_B.