Numerical solution of well flow in unconfined aquifers using a transformation of the Spalding-Patankar type

This report presents the results of a study to develop a finite difference procedure for solving the parabolic partial differential equation describing the flow of ground water toward a well in an unconfined aquifer. The approach differs from previous efforts in that a transformation is applied to the equation which was originally developed for the solution of two-dimensional boundary layer flows. The transformation is introduced to control grid spacing as the maximum value of the spatial variable varies over a wide range. A computer program was written to perform the solution and results for sample cases are presented.