Flow into the control-volume is calculated as follows, assuming constant density:

p(Ue*Ae - Uw*Aw) in the x-direction and p(Un*An - Us*As).

The convected quantity, e.g. temperature, is then calculated as follows at their respective faces as

East face TP                                      West face TW

North face TP                                    South face TS.

What are the shortcomings of such an approximation, in the

light that the variation of the variable T in the coordinate directions might not be linear.

What other approximations can be considered if the flow at the faces, i.e. Ue, Uw, Un, Us are not at 90 degrees to their respective faces, i.e. that flow is at an angle to the grid.

Any ideas