Two-dimensional flow through large numbers of circular inhomogeneities

An implicit analytic solution is presented for two-dimensional groundwater flow through a large number of non-intersecting circular inhomogeneities in the hydraulic conductivity. The locations, sizes and conductivity of the inhomogeneities may be arbitrarily selected. The influence of 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 discharge potential from all other elements. Using a least squares formulation for the boundary conditions 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 precision and speed allows the development of a numerical laboratory for investigating two-dimensional flow and convective transport. (C) 1999 Elsevier Science B.V.