Robustness and efficiency of iteration schemes for variably saturated flow across the range of soils, initial and boundary conditions found in practice

Abstract

Water flow in partially saturated porous media is of importance in many disciplines such as hydrology, agriculture, environmental management or geotechnical engineering. A robust and accurate solution methodology applicable across the range of soils, initial and boundary conditions found in practice is difficult to identify. Three mass conservative iteration schemes for the approximation of the flow equation in partially saturated porous media are evaluated considering large contrasts in soil texture, initial moisture and boundary conditions typically found in real world application. The three schemes reviewed are the well established modified Picard algorithm (Celia-Scheme), and two promising approaches the L-Scheme and the Casulli-Scheme. A systematic variation of soil texture and initial moisture in an intense rainfall infiltration scenario is set up in order to consider the numerical challenges associated with high non-linearity. The present analysis provides insights into robustness and efficiency in solving variably saturated flow across the range of soils, initial and boundary conditions found in practice. Casulli’s scheme, in particular, provides an acceptable compromise between robustness and execution duration even under the severest conditions investigated, while the other schemes sacrifice one for the sake of the other. The authors believe that advances in the development of numerical schemes for partly saturated flow require the kind of methodology presented here in combination with relevant benchmark problems in order to enable a fair evaluation and comparison of numerical techniques across the related disciplines.