Unsaturated Flow Through Spherical Inclusions with Contrasting Sorptive Numbers

Abstract

and for unsaturated flow through inclusions (Warrick and Knight, 2002, 2004;Bakker and Nieber, 2004). The analytic element method (AEM) is used to model unsaturated All the AEM solutions for unsaturated flow made flow through a spherical inclusion of contrasting hydraulic properties. use of the Gardner (1958) function (also known as the The steady state Richards' equation is combined with the Gardner model Philip model) to describe the relations between the hyfor unsaturated hydraulic conductivity to form the Helmholtz equation. The later is solved by means of the AEM. The background and inclu-draulic conductivity and the pressure head. This allows sion materials are assumed to have different saturated hydraulic conthe transformation between Richards' equation to the ductivities and different sorptive numbers; hence, the conditions are Helmholtz equation (using the matric flux potential, or more general than treatments of spherical inclusions. Continuity of the the so-called Kirchhoff potential). Warrick and Knight interfacial head boundary condition leads to a nonlinear system of (2002, 2004) were the first to introduce the AEM to deequations, whose solution requires an iterative solution. Analysis inscribe unsaturated flow. They considered circular and cludes the effect of the hydraulic properties and of the background flux spherical inclusions with a uniform distribution of the and evaluation of computational efficiency for contrasting hydraulic Gardner coefficient ␣. Bakker and Nieber (2004) extended properties. To examine water contents, a methodology is presented the solution by considering circular inclusions (and cirfor matching Gardner and van Genuchten parameters. The new solu-cular drains) and allowing contrasts in ␣. This is a valution is more realistic than the previous solution for a spherical inclusion with a sorptive number the same as the background but is computa-

Modeling Coupled Surface–Subsurface Flow Processes: A Review

“…It is customary to represent these two conditions as velocity and its normal gradient; however, other representational options are equally valid. In many of the cases that will be presented below, boundary conditions have been represented in terms of flux and energy (head), which is more customary in fields such as porous media internal boundaries (see, e.g., Janković and Barnes, 1999; Furman and Neuman, 2003; Furman and Warrick, 2005). The different approaches presented above result from (i) the different formulations of the flow equations in the two regions (i.e., mostly due to the treatment of the porous medium as a continuum); (ii) the difficulty in defining a sharp interface; and (iii) the desire to simplify the boundary conditions to allow practical application.…”

Correspondence of the Gardner and van Genuchten–Mualem relative permeability function parameters

“…Several methods for translating the van Genuchten parameters to Gardner parameters (and vice versa), have been proposed [e.g., Birkholzer et al , 1999; Furman and Warrick , 2005; Morel‐Seytoux et al , 1996; Rucker et al , 2005]. Brief summaries of these approaches are given in the next subsection.…”

“…The most straightforward approach for estimating the Gardner parameters ψ b and α G using the known vGM k r ‐ ψ function involves minimizing the differences between the Gardner and van Genuchten relative permeability curves [e.g., Birkholzer et al , 1999; Furman and Warrick , 2005]. The number and distribution of matching points for least squares fitting can be chosen to provide the best match in the regime of interest.…”