Comparison of Equivalent Conductivities for Numerical Simulation of One‐Dimensional Unsaturated Flow

Abstract

Gasto et al., 2002) have also been implemented successfully. Despite the promising results reported by the differ-Water flow in unsaturated porous media is usually simulated using ent authors, these schemes have not been widely adopted the Richards equation in combination with some numerical method for spatial and temporal discretization. In this study we implement a because of the additional complexity and/or computamixed hybrid finite element solution with different formulations for tional effort involved. Moreover, little information exists the equivalent hydraulic conductivity in an attempt to more accurately about the treatment of interblock conductivities when simulate variably saturated flow. The advantages of a quadrature rule the two neighboring nodes are located in soil layers with are demonstrated for simulations of sharp infiltration fronts. Results contrasting hydraulic properties (Zaidel and Russo, 1992; show the importance of selecting an appropriate equivalent conductiv-Brunone et al., 2003), a situation which is commonly ity. Geometric, weighted and integrated formulations produced better encountered in the field. The accuracy of unsaturated solutions than a traditional scheme using a mean conductivity calculated flow predictions may then very much depend on how with a mean pressure head. Two illustrative test cases are considered interlayer conductivities are evaluated. for infiltration in initially dry homogeneous and heterogeneous soils This study is focused principally on an alternatively subject to both Dirichlet and variable Neumann boundary conditions. The accuracy and computational efficiency of the proposed algorithm numerical approach referred to in the literature as the with the different conductivity formulations is demonstrated by means mixed hybrid finite element (MHFE) method (Chavent of comparisons with a finite difference approach using various inter-

Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

“…The Chinese loam soil was fitted to the GE function (Pei 2003). As represented by the vG function, the Glendale clay loam (Hills et al 1989) was widely used as a test problem (e.g., Warrick 1991), the New Mexico clay (Celia et al 1990) was also Celia et al (1990) tested in previous work (e.g., Williams and Miller 1999), and the Berino loamy fine sand (Hills et al 1989) was tested by Belfort and Lehmann (2005). Besides the referred media in Table 2, the wide ranges of parameters, i.e., α GE , β, and m, were used to show the variation of k H .…”

“…As listed in Table 3, k app derived from the mean k were widely used and tested in vertical unsaturated flow by Haverkamp and Vauclin (1979), Warrick (1991), Baker (1995Baker ( , 2006, and Belfort and Lehmann (2005). Moreover, k app obtained from mean h were also used and tested by Haverkamp and Vauclin (1979) and Baker (2006), while k app based on the mean S e were rarely used and only the k AM-S was tested by Zaidel and Russo (1992), Miller et al (1998), andWilliams et al (2000).…”

“…A number of estimation methods have been reviewed (Haverkamp and Vauclin 1979;Schnabel and Richie 1984;Warrick 1991;Ross 1990;Zaidel and Russo 1992;Oldenburg and Pruess 1993;Srivastava and Guzman-Guzman 1995;Desbarats 1995;Romano et al 1998;Baker et al 1999;Gastó et al 2002;Brunone et al 2003;Belfort and Lehmann 2005;Baker 1995Baker , 2000Baker , 2006. By assuming constant flux between adjacent blocks, Warrick (1991) first suggested an effective interblock conductivity which was later denoted as k H for the horizontal flow and k V for the vertical flow by Baker (1995).…”

Simulation of flows in heterogeneous porous media of variable saturation

“…There is a vast literature on the numerical study of the Richards equation, both with the finite difference method and with finite element method see [8][9][10][11][12][13][14][15].…”

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

“…Several techniques had been proposed in the literature for the computation of interface conductivity [20], but no clear conclusions have been drawn. The arithmetic mean is used in many studies and models, including the widely accepted HYDRUS model, but it can lead to spurious oscillations in the solution.…”