On the solution of transient free-surface flow problems in porous media by finite-difference methods

Abstract

Numerical solutions are obtained for a few initial-boundary-value problems in free-surface, saturated liquid flow through porous media. The “exact” differential equations governing the problems have been approximated by finite-difference equations, and the resulting system of algebraic equations is solved by using an automatic digital computer. Only two-dimensional, homogeneous and isotropic flow models — including infiltration — are dealt with, but in principle there is little difficulty in extending the models to nonhomogeneous and anisotropic media. Though also possible in principle, an extension to three dimensions will demand a drastic increase in the necessary storage space of the computer. The question of computational stability of the difference schemes adopted is considered. Good agreement with some results of other calculations is found for the two distinct models that have been studied — one “ditch drainage” and one earth dam model.