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2D implementation

  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).


Tatiana Tijanova
Wed Mar 26 10:36:42 MET 1997