3D implementation

  We give here two ways to describe the velocities in the physical domain:

(i)

with Cartesian velocity components,

(ii)

with normal and tangential components.

In the present version, only the first approach is implemented.

(i)

If the Cartesian velocity components are prescribed we can compute the contravariant components in the following way:

 

(ii)

Normal and tangential components are prescribed on the plane where is constant. The scalar products and with the tangential vectors and are given by the user. See Figure 7.2.

  
Figure: The scalar products and and tangential vectors and are prescribed. Here is .

From and we can compute and by:

  

where

  

Formula (7.7) makes no sense if the tangential vectors and are linear dependent, so they have to be linear independent.
The given and are implemented in almost the same way as in the 2D-case.