The tangential velocity and normal stress are prescribed at the boundary, i.e.:
From equation (7.7) it is clear that we can calculate 
and 
as 
and 
are zero, otherwise we
have to make an assumption about and . In the
remainder of this section we assume that
at the boundary.
From 
and equation (7.22) follows the stress 
at the boundary in the computational domain.
Boundary condition (7.45) influences the two ''tangential''
velocity cells (see Figure 7.5) and the ''normal'' velocity
half-cell (see Figure 7.6).
The 
and 
''tangential'' cells (bottom boundary) are built in
a similar way as the inner cells. The only difference is that virtual
velocity components and pressures are eliminated by linear extrapolation.
For example for the bottom boundary we get:
The normal velocity half-cell at the bottom boundary. The discretization of the convective term gives
Terms with the factor 
are the only terms where we need a
linearization procedure, since 
and 
are given at the
boundary.
We use the following discretization of the stress tensor:
where 
is given by 
. So
the right-hand side gets the contribution:
The virtual velocities introduced by formula (7.51) are eliminated
by linear extrapolation. Just as in 2D is the pressure evaluated in the
points (1,0,1), (-1,0,1), (0,1,1) and (0,-1,1) instead of (1,0,0),
(-1,0,0), (0,1,0) and (0,-1,0).
