Abstract

The analytic element method (AEM) is used to model unsaturated flow through a spherical inclusion of contrasting hydraulic properties. The steady state Richards' equation is combined with the Gardner model for unsaturated hydraulic conductivity to form the Helmholtz equation. The later is solved by means of the AEM. The background and inclusion materials are assumed to have different saturated hydraulic conductivities and different sorptive numbers; hence, the conditions are more general than treatments of spherical inclusions. Continuity of the interfacial head boundary condition leads to a nonlinear system of equations, whose solution requires an iterative solution. Analysis includes the effect of the hydraulic properties and of the background flux and evaluation of computational efficiency for contrasting hydraulic properties. To examine water contents, a methodology is presented for matching Gardner and van Genuchten parameters. The new solution is more realistic than the previous solution for a spherical inclusion with a sorptive number the same as the background but is computationally more tedious.

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