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RAPID AND NUMERICALLY STABLE SIMULATION OF ONE‐DIMENSIONAL, TRANSIENT WATER FLOW IN UNSATURATED, LAYERED SOILS

We present a rapid numerical solution for vertical, transient flow of water in unsaturated soil. The model is labeled the moving mean slope model (MMS model), because it uses the slope of the natural log of the hydraulic conductivity (K) versus soil-water potential (ψ) curve as a dynamic parameter. The MMS model is developed from a model for flow in homogeneous, relatively wet soils presented by Wind and von Doorne (1975). The model can simulate transient flow in homogeneous and heterogeneous soils correctly for any rang e of soil-water content. This has been validated against semianalytical solutions and solutions obtained with traditional finite-difference and finite-element models. A Courant number analysis method is presented to make direct comparisons of criteria for avoiding numerical errors for the MMS model compared with traditional finite-difference models. For coarse-textured soils, the MMS model uses about the same computer time as the traditional finite-difference and finite-element models. For soils ranging from fine-textured to medium-textured, the MMS model is one to several orders of magnitude faster than the traditional numerical models.