WWRC 86-17
A Finite-Element Collocation Method for Variably Saturated Flow in Two Space Dimensions
Abstract
This paper introduces a finite-element collocation technique for solving the equation governing
two-dimensional flow in a variably saturated porous medium. The scheme uses a mass-conserving
formulation of Richards' equation as the basis for the finite-difference time-stepping method. Collocation in
tenser-product spaces of Hermite cubics yields a computationally efficient finite-element approximation
of the spatial derivatives. A Newton-like iteration gives a temporally stable implicit scheme. The paper
examines two sample problems, including an initial boundary-value problem involving subsurface irrigation.
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