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- The finite water-content vadose zone flux method represents a one-dimensional alternative to the numerical solution of Richards' equation for simulating the movement of water in unsaturated soils. The finite water-content method solves the advection-like term of the Soil Moisture Velocity Equation, which is an ordinary differential equation alternative to the Richards partial differential equation. The Richards equation is difficult to approximate in general because it does not have a closed-form analytical solution except in a few cases. The finite water-content method, is perhaps the first generic replacement for the numerical solution of the Richards' equation. The finite water-content solution has several advantages over the Richards equation solution. First, as an ordinary differential equation it is explicit, guaranteed to converge and computationally inexpensive to solve. Second, using a finite volume solution methodology it is guaranteed to conserve mass. The finite water content method readily simulates sharp wetting fronts, something that the Richards solution struggles with. The main limiting assumption required to use the finite water-content method is that the soil be homogeneous in layers. The finite water-content vadose zone flux method is derived from the same starting point as the derivation of Richards' equation. However, the derivation employs a hodograph transformation to produce an advection solution that does not include soil water diffusivity, wherein becomes the dependent variable and becomes an independent variable: where: is the unsaturated hydraulic conductivity [L Tâ1], is the capillary pressure head [L] (negative for unsaturated soil), is the vertical coordinate [L] (positive downward), is the water content, (â) and is time [T]. This equation was converted into a set of three ordinary differential equations (ODEs) using the Method of Lines to convert the partial derivatives on the right-hand side of the equation into appropriate finite difference forms. These three ODEs represent the dynamics of infiltrating water, falling slugs, and capillary groundwater, respectively. (en)
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- The finite water-content vadose zone flux method represents a one-dimensional alternative to the numerical solution of Richards' equation for simulating the movement of water in unsaturated soils. The finite water-content method solves the advection-like term of the Soil Moisture Velocity Equation, which is an ordinary differential equation alternative to the Richards partial differential equation. The Richards equation is difficult to approximate in general because it does not have a closed-form analytical solution except in a few cases. The finite water-content method, is perhaps the first generic replacement for the numerical solution of the Richards' equation. The finite water-content solution has several advantages over the Richards equation solution. First, as an ordinary differentia (en)
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- Finite water-content vadose zone flow method (en)
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