The slip boundary condition is equivalent to tangential stress as well as
normal velocity component given.
The treatment of this type of boundary conditions is the subject of
[24].
All formulae in this section are copied from that report.
The normal velocity given implies given by the relation
(7.1). The tangential stress given, however, does not automatically
imply that a component of the contravariant stress tensor is prescribed. In fact it only implies a linear combination
between stress components at the boundary through the relation
Since the normal velocity component is given no normal half cells are
introduced.
The discretization of the convective terms implies the evaluation of virtual
velocities by linear extrapolation. The discretization of the stress tensor
is given by
The linear extrapolation formula for the velocities is given by
The term is equal to:
where the first term is given and the second term involves virtual
velocities and pressures that can be eliminated by (7.54) resp.
(7.3).