A three‐dimensional finite‐element model for simulating water flow in variably saturated porous media

Abstract

A three‐dimensional finite‐element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an “influence coefficient” technique that avoids costly numerical integration. Spatial discretization of a three‐dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite‐element model. The first four examples concern one‐ and two‐dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three‐dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three‐dimensional situations involving seepage faces and anisotropic soil media.