As (5.13) is normally not diagonal-dominant it is eliminated in a pre-pass. It is important to note, that in this case the structure of the equation system changes. The constitutive relation for is now given by (5.13) whereas for by (5.14), or vice-versa. This is accomplished by the following transformation matrix
The fluxes contained in f can also be used to calculate the total interface flux FI by setting up the following equation:
|f = fS + FI = 0||(5.15)|
with i running over all interface points.