Numerical simulations of one-dimensional infiltration into layered soils with the Richards equation using different estimates of the interlayer conductivity

Transient water flow processes in unsaturated soils are usually modeled using the Richards equation. This paper compares several numerical approximations to this equation for vertical infiltration in layered soil profiles. Three formulations of the governing flow equation (i.e., the h-based, _-based, and mixed forms) are compared for the critical test problem of infiltration into a layered soil profile with initially relatively low soil water contents. An efficient, yet relatively simple weighting algorithm is employed that improves the estimation of the interlayer hydraulic conductivity in an h-based finite-difference formulation. Results highlight improvements in the mass conservative properties of this model, which is termed the H-IL model. A comparison is then performed between the finite-difference H-IL model and a finite-element model for infiltration toward a water table. The H-IL model was found to be computationally very efficient for this test problem. For both illustrative flow examples, the different numerical models were evaluated in terms of their ability to reproduce an exact solution developed by Srivastava and Yeh (1991) in their work on one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.