MODELING 3-DIMENSIONAL FLOW ABOUT ELLIPSOIDAL INHOMOGENEITIES WITH APPLICATION TO FLOW TO A GRAVEL-PACKED WELL AND FLOW THROUGH LENS-SHAPED INHOMOGENEITIES

Analytic functions are superimposed to model three-dimensional steady groundwater flow in regions containing one or more inhomogeneities shaped like prolate or oblate ellipsoids of revolution. Each function and the sum of such functions are solutions of Laplace's equation, the governing differential equation for steady groundwater flow. The functions are implemented in manner that provides exact continuity of flow across the entire boundary of each inhomogeneity. In general, continuity of head is provided at specified control points on the boundary and is approximated between control points. For the case of one inhomogeneity in a uniform flow field, it turns out that there is exact continuity of head across the entire surface of the inhomogeneity. The method is implemented in a computer program written by the author. Two applications are demonstrated: (1) flow to a gravel-packed well and (2) flow through a series of lens-shaped inhomogeneities. The examples demonstrate that the approximation of continuity of head can be made acceptable for many problems. A possible application of the techique would be testing various theories regarding contaminant migration and dispersion by simulating flow and chemical diffusion through large numbers of lens-shaped inhomogeneities.