Comparison of averaging methods for interface conductivities in one-dimensional unsaturated flow in layered unsaturated soils

Numerical simulations of water flow through unsaturated soils have been well studied but very few studies have addressed water movement across soil interfaces by imposing continuity of both flux and pressure head. Imposing continuity of both head and flux leads, at a local discrete level, to a nonlinear interface equation which may exhibit multiple solutions if the spatial discretization is not fine enough, for example during infiltration with sharp fronts or in the presence of very dissimilar soil layers. The non-uniqueness of solutions of the interface equation can lead to numerical errors and/or numerical oscillations. We use a staggered finite difference approach with cell-centered hydraulic conductivities estimated by averaging nodal conductivities. We evaluate the impact of several averaging schemes (arithmetic, harmonic, geometric and log-mean) on the occurrence of multiple solutions and associated numerical issues. The resulting numerical schemes are compared in terms of their propensity to trigger multiple roots at soil interfaces. Our results show that the choice of averaging scheme does affect the occurrence of multiple solutions and long term behavior of the numerical solution. In particular, our simulations confirm that the averaging schemes associated with larger interface conductivities (log-mean and arithmetic mean) are less likely to suffer from non-uniqueness issues of the interface problem.