Approximation of internodal conductivities in numerical simulation of one-dimensional infiltration, drainage, and capillary rise in unsaturated soils

When the unsaturated flow equation is solved with the finite difference method, the water flux between two adjacent nodes of the grid is approximated with a discrete form of Darcy's law. It requires the average value of the hydraulic conductivity in the considered grid block. Since the hydraulic conductivity in unsaturated soil is a highly nonlinear function of the water potential, the nodal conductivities can vary by multiple orders of magnitude, which makes the choice of the appropriate averaging procedure a nontrivial task. In this paper we present a new method to calculate the internodal conductivity for an arbitrary type of the conductivity function and arbitrary large grid size. It is based on the analysis of approximate profiles of the water potential head for steady flow between nodes. Numerical experiments show that the method is reasonably accurate for a wide range of soil types, for both steady and unsteady flow simulations.