Analysis of Nonsteady Flow with a Free Surface Using the Finite Element Method

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Abstract
A new iterative, numerical approach to nonsteady flow of groundwater with a free surface using the finite element method has been developed. The method is unconditionally, stable and therefore requires only a small number of time steps to reach the steady state. It can handle problems in which the free surface is discontinuous and portions of the free surface are vertical or nearly vertical. Infiltration or evapotranspiration at the free surface is handled with ease, and the effect of the unsaturated zone can be taken into account indirectly by using the concept of delayed yield from storage. In addition to gravity drainage, the method takes into consideration storage due to the elastic properties of the saturated porous medium. In problems involving flow to a well operating at a prescribed rate, both storage in the well and the actual distribution of velocities along the well bore are taken into account. The method can be applied to a wide variety of problems involving complex boundaries and arbitrary degrees of heterogeneity and anisotropy. Several examples are included to demonstrate some of the features of this new approach.