Selection of Intermodal Conductivity Averaging Scheme for Unsaturated Flow in Homogeneous Media

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, which causes a steep pressure gradient and great variation of hydraulic conductivity occurs across the wetting front during the infiltration of water. So, the averaging method applied to compute hydraulic conductivity between two adjacent nodes of the computational grid is one of the most important issues influencing the accuracy of the numerical solution of one-dimensional unsaturated flow equation i.e., Richards’ equation. A number of averaging schemes such as arithmetic, geometric, harmonic and arithmetic mean saturation have been proposed in the literature for homogeneous soil. The resulting numerical schemes are evaluated in terms of accuracy and computational time. It can be seen that the averaging scheme in the framework of arithmetic approaches favorably to other methods for a range of test cases.