Three-dimensional flow through large numbers of spheroidal inhomogeneities

An implicit analytic solution is presented for three-dimensional (3D) groundwater flow through a large number of nonintersecting spheroidal inhomogeneities in the hydraulic conductivity. The locations, dimensions, and conductivity of the inhomogeneities may be arbitrarily selected. The specific discharge potential due to each inhomogeneity is expanded in a series that satisfies the Laplace equation exactly. The unknown coefficients in this expansion are related to the coefficients in the expansion of the combined specific discharge potential from all other elements. Using a least-squares formulation for the boundary conditions, a superblock approach, and an iterative algorithm, solutions can be obtained for a very large number of inhomogeneities (e.g. 10,000) on a personal computer to any desired precision, up to the machine's limit. Such speed and precision allows the development of a numerical laboratory for investigating 3D flow and convective transport. (C) 1999 Elsevier Science B.V.