A Finite-element Collocation Method for Variably Saturated Flow in Two Space Dimensions

1. INTRODUCTION This paper presents a finite-element collocation scheme for simulating variably saturated flows in two space dimensions. The scheme is an extension of a mass conserving one-dimensional formulation presented earlier [Allen and Murphy, 1985). The present exposition gives a complete description of work reported more briefly in the work by Murphy and Allen [1986]. Among the key features of the methodology presented here are (1) the particular piecewise polynomial approximations used to represent the spatial heterogeneities in hydraulic conductivity, moisture content, and specific moisture capacity, and (2) the implementation of a Newton-like iterative scheme that ensures a stable, consistent time-stepping procedure in the presence of strong nonlinearities. The equation we solve is the two-dimensional Richards