Comparison of Averaging Methods for Interface Conductivities in One-dimensional Unsaturated Flow in Layered Soils

The water flow in unsaturated soils is governed by Richards equation, a nonlinear parabolic partial differential equation. In a layered unsaturated soil, enforcing the continuity of both pressure head and flux across the interface of distinct soil materials leads to a non-linear interface equation. This interface equation may exhibit multiple solutions. Using different averaging methods for cell-centered hydraulic conductivities impacts the ill-posedness of this interface problem and therefore affects the numerical simulations of transient unsaturated flow. Four averaging methods for cell-centered conductivities (arithmetic, harmonic, geometric or log-mean) are compared in this study. The choice of averaging schemes impacts the limit of discretization size that is needed to guarantee a unique solution of the interface equation. Numerical experiments confirm that the averaging schemes leading to larger interface conductivity averages (log-mean) are less likely to be affected by the non-uniqueness of solutions to the interface problem.