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4 Material Balance Difference Equations in Two and Three Dimensions     continued...

Suppose that the finite difference block whose center is at is to be treated as the control block in a material balance argument. Then it is convenient to refer to the sides of the block by reference to the points of the compass. See Figure 4.

Figure 4: Control region with compass labeled faces.

With this compass-point notation imposed on the control cell with center , various FDEs can be derived from the following statement of conservation:

In the absence of sources or sinks, the change of material content in the finite difference cell is equal to the flow of material in across the west face minus the flow out across the east face, plus the flow in across the south face minus the flow out across the north face.

Applying this conservation principle we obtain the following.