Selection of Intermodal Conductivity Averaging Scheme for Unsaturated Flow inHomogeneous Media

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone toconvergence difficulties. Many aspects can give rise to such difficulties, like very dry initialconditions, which causes a steep pressure gradient and great variation of hydraulic conductivity occursacross the wetting front during the infiltration of water. So, the averaging method applied to computehydraulic conductivity between two adjacent nodes of the computational grid is one of the mostimportant issues influencing the accuracy of the numerical solution of one-dimensional unsaturatedflow 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 beseen that the averaging scheme in the framework of arithmetic approaches favorably to other methodsfor a range of test cases