The interpolation of the velocity is performed in three steps.
In the first step the Cartesian velocity is computed in the cell centre.
First the fluxes and are averaged according to
see Figure 11.3 for the notations. Next the fluxes
Figure 11.3: Cell with fluxes and centroid
are transformed to Cartesian velocity components using:
hence
In the second step each of the components is interpolated to the vertices
by exactly the procedure described for scalars in 11.1.
Finally at the boundary essential boundary conditions, if present, are
substituted in order to avoid unnecessary interpolation erors.