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3D implementation

  In this condition the normal velocity and tangential stress with are prescribed. So we don't need ''normal'' velocity half-cells. We have only to consider the two ''tangential'' cells. For the remainder of this section is the slip boundary condition given on the bottom boundary.
The discretization of the convective terms is given by:

 

Since is prescribed at the bottom boundary we do not have to use a linear approximation for (see [24], formula (3.9)):

 

The discretization of the stress tensor is given by:

 

The virtual velocities introduced by formula (7.58) are eliminated by linear extrapolation, i.e. using formula (7.25), (7.26) and (7.27).
The term in (7.58) is for -cell) equal to:

 

where , so:

 

Term in (7.58) is for equal to:

 

where , so:

 

The factors and are calculated with formula (7.24a)-(7.24b).
The in (7.60) and (7.62) involves virtual velocities and pressures that can be eliminated by (7.25)-(7.27) and (7.48).
Before treating the boundary conditions for the scalar equations we shall first consider the special cases where we have a transition of one type of a boundary condition to another as well the case of a corner of the region.


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