Flux-Based Alternative Formulation for Variably Saturated Subsurface Flow

Abstract

Finite-element and finite-difference solutions to different forms of the Richards equation can exhibit stability problems as well as mass balance errors. These problems are more pronounced for sharp wetting fronts in soils with very dry initial conditions and at material interfaces for layered soil profiles. The pressure head form can suffer from large mass balance errors while the moisture content form conserves mass perfectly but has difficulty handling material boundaries in layered soil profiles and near saturation conditions. This paper presents a conservative mixed formulation for the solution of the Richards equation of unsaturated flow by the finite-element method in which the discharge velocity (volumetric flux) and pressure head are the primary field variables. Solution techniques for various boundary conditions including prescribed constant pressure head and constant flux are also presented. The ability of the formulation to handle variably saturated domain and material heterogeneity is also established. Example solutions for infiltration into homogeneous and heterogeneous unsaturated and variably saturated soil profiles are compared with finite-element and finite-difference solutions of pressure head and mixed form of Richards equation. Results indicate that the alternative formulation is mass conservative, stable, and can better handle heterogeneous boundaries and variably saturated flow domains.