Modeling of Groundwaterflow with Maple

The Method

Based on a method that appeared in Numerical Functional Analysis and Optimization, by Shivakumar, Williams and Ye, we made a maple file for the modeling of saturated, steady-state groundwaterflow in a non-trivial domain (see figure on the right). The method uses seperation of variables to reduce the problem to the construction af a Grammian matrix. In the maple file we construct the resulting matrix equation, solve it to the unknowns, and plot the solution.
As said, it is an extension of the original paper. To be specific, the groundwaterflow is calculated in a finite domain (depth T) for the basic equation:
Formule

with on the top Dirichlet boundary condition (head = z, the elevation, so atmospheric pressure), and impenatrable other boundaries. As an extra, changed borderconditions are also handled: a Dirichlet boundary at the bottom.
The maple files are general. You can change the parameters in the beginning and rerun the files to get different results !

Maple files

The maple files can (normally) be saved by right clicking on them, and selecting "save as". Following files are given :

Groundwaterflow in an infinite domain generalinf.mws. This is the original article in a maple file solution. Important to note is the error in correspondance to the error in the extended solution.
Groundwaterflow in a finite domain, generalfin.mws (our own work). With this file, practical groundwaterflows can be studied. As an example, the same file, applied to a classical result of J. Toth from 1962 that appeared in Journal of Geophysical Research : toth_2c.mws, which is example 2c from the original article.
Just for fun, an extra expansion to the calculation. What happens if the bottom of our domain is a percolating boundary, meaning a Dirichlet boundary condition can be imposed there. The result in general_finleak_ext.mws.

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