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Finite Element Analysis of Two-Dimensional Flow in Soils Considering Water Uptake by Roots: I. Theory¹

ABSTRACT

The problem of two-dimensional nonsteady flow of water in unsaturated and partly saturated porous media is solved by a Galerkin-type finite element approach. Particular emphasis is placed upon the simulation of atmospheric boundaries and of water uptake by plant roots. The finite element method is shown to have several advantages over conventional finite difference techniques. It can easily handle nonuniform flow regions having irregular boundaries and arbitrary degrees of local anisotropy. Nonlinear atmospheric boundary conditions along evaporation or infiltration surfaces and along seepage faces are handled by a unique procedure. This iterative procedure relies on the ease with which flux normal to any boundary of the flow region is assigned in the finite element approach. Our experience with this method indicates that rapid rates of convergence can be achieved in many cases. Part I of the paper presents the theory, whereas Part II is devoted to a field test of the finite element method and to a comparison of the results with those obtained from a one-dimensional finite difference model.

¹ Contribution from the Division of Soil Physics, Institute of Soils & Water, Agricultural Research Organization, Bet Dagan, Israel. 1974 Series, no. 193-E.

² Research Hydrologist, Inst. of Soils and Water, ARO, Bet Dagan, Israel; Soil Scientist, on leave from the Inst. for Land & Water Management Research, Wageningen, The Netherlands; and Soil Scientist, Inst. of Soils & Water, ARO, Bet Dagan, Israel, respectively.

Received for publication June 10, 1974. Accepted for publication October 7, 1974.