We will use finite differences to solve the ground-water flow equations. Using the finite difference approach, we divide our system into many pieces (sometimes called grid blocks, cells or elements). This is called discretizing or discretization. Each cell can be represented by only one value of either an independent or dependent variable (that is, only one value each of hydraulic conductivity, storage coefficient, head, and flow rate applies to each cell).

The ground-water flow equation is written for each cell. All but one unknown is defined for each cell, that is, we must know either the head or the flow rate for each cell. This is easier than it seems because we know that the net flow for all internal cells must be zero, because the inflow must balance with the outflow and the change in storage.

Next we solve the equations simultaneously to determine the unknown at each cell. Often the models are so large that we cannot solve all the equations at once in the available memory of our computer, consequently there are a variety of matrix solution schemes that may be called upon to approximate the solution. In this unit, we will discuss finite differences and the items that you will need to be aware of in order to achieve an acceptable approximate solution.