Analytical Solutions Using Integral Formulations and Their Coupling with Numerical Approaches

Analytical and numerical approaches have their own distinct domains of merit and application. Unfortunately there has been a tendency to use either one or the other even when their domains overlap. Yet there is definite advantage in combining the two approaches. Being relatively new this emerging technique of combining the approaches is, at this stage, more of an art than a science. In this article we suggest approaches for the combination through simple examples. We also suggest that the integral formulation of the analytical problems may have some advantages over the differential formulation. The differential formulation limits somewhat the range of linear system descriptions that can be applied to a variety of practical problems. On the other hand the integral approach tends to focus attention to overall integrated behavior and properties of the system rather than on minute details. This is particularly useful in the coupling with a numerical model as in practice it generally deals also with only the integrated behavior of the system. The thesis of this article is illustrated with some simple stream-aquifer flow exchange examples.