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

Abstract

Water flow in unsaturated porous media is usually simulated using the Richards equation in combination with some numerical method for spatial and temporal discretization. In this study we implement a mixed hybrid finite element solution with different formulations for the equivalent hydraulic conductivity in an attempt to more accurately simulate variably saturated flow. The advantages of a quadrature rule are demonstrated for simulations of sharp infiltration fronts. Results show the importance of selecting an appropriate equivalent conductivity. Geometric, weighted and integrated formulations produced better solutions than a traditional scheme using a mean conductivity calculated with a mean pressure head. Two illustrative test cases are considered for infiltration in initially dry homogeneous and heterogeneous soils subject to both Dirichlet and variable Neumann boundary conditions. The accuracy and computational efficiency of the proposed algorithm with the different conductivity formulations is demonstrated by means of comparisons with a finite difference approach using various interblock conductivity averages.