Abstract
The analytic element method, first developed for modeling flow in saturated porous media, is adapted to the solution of the governing equation for steady flow in unsaturated porous media. The governing equation for steady-state unsaturated flow is made amenable to analytic element solution through transformation with the Kirchhoff integral, representation of the hydraulic conductivity by an exponential function of the pressure head, and use of a coordinate transformation. A number of analytic elements are available for the resulting modified Helmholtz equation; analytic element equations are presented for uniform flow, cylindrical drains, and cylindrical inhomogeneities. The analytic element solution allows for the analytic evaluation of the pressure head, saturation, and Darcy flux at any point in the vadose zone. The applicability of the analytic element method to simulate unsaturated flow is demonstrated by solving for several cases of steady flow in a region containing arbitrarily located cylindrical inhomogeneities, and for flow in a region containing one cylindrical inhomogeneity and two cylindrical drains.
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