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Application of Mixed Finite Element Method to One-Dimensional Unsaturated Flow

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  Paper number  032112,  2003 ASAE Annual Meeting . (doi: 10.13031/2013.14005) @2003
Authors:   Debasmita Misra, John L. Nieber
Keywords:   Unsaturated flow, Darcy flux, Richards equation, Mixed finite element method

Flow in the unsaturated porous media is governed by a strongly nonlinear diffusion type equation with a nonlinear, forced convection term due to gravity. These features make it particularly difficult to solve by any means. The flow induced heterogeneity and the specific moisture capacity of the medium make the governing equation of flow highly non-linear due to the dependence of these parameters on the pressure and the moisture content distribution in the medium.

The velocity at which water flows through the unsaturated zone is at all times less than or equal to that in a porous medium saturated with the fluid. As a result, the chemicals transported by the water find more resident time in the medium for reactions, transformations and attenuations. This could have significant impact on the quality of water reaching the ground water table or on the chemicals absorbed by the plants or escaping to the atmosphere in volatile form.

Accurate simulation of Darcy flux is essential to simulate contaminant transport in the unsaturated zone accurately. The mixed finite element method has been used to obtain highly accurate flux distribution in unsaturated zone flow applications. The objective of this paper is to present a simplified conceptual description of the mixed finite element method as applied to unsaturated flow modeling, to compare the solutions obtained from the method to those of the conventional finite element methods and to analyze any special properties of the solutions obtained from the mixed finite element methods. It has been shown in this paper that the solutions obtained from the mixed finite element method are highly accurate in rapidly changing flux distributions and heterogeneous flow distributions even when relatively coarse grids are used to obtain the solution.

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