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Ursino, Nadia

doi:10.1023/a:1006688232755

Cited by 10 publications

(2 citation statements)

References 18 publications

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“…Notice that a similar approach was applied by Srivastava and Yeh [34], who introduced an even more simple version of (23) for an exponential dependence of θ on h, and then followed also by other researchers for theoretical studies or to validate numerical models (see, e.g., [35][36][37], among the others).…”

Section: K-based Equationmentioning

confidence: 99%

Modeling Water Flow in Variably Saturated Porous Soils and Alluvial Sediments

Giudici

2023

Sustainability

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The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content (θ) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for θ), and the Richards Equation (for h). The other two forms can be given for generalized matric flux potential (Φ) and for hydraulic conductivity (K). The latter two cases are shown to limit the non-linearity to multiplicative terms for an exponential K-to-h relationship. Different types of boundary conditions are examined for the four different formalisms. Moreover, remarks given on the physico-mathematical properties of the relationships between K, h, and θ could be useful for further theoretical and practical studies.

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Section: K-based Equationmentioning

confidence: 99%

Modeling Water Flow in Variably Saturated Porous Soils and Alluvial Sediments

Giudici

2023

Sustainability

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“…Such interest is confirmed in the milestone paper Philip (1989), motivated since, even for multidimensional unsaturated flows, the steady solutions are approached rapidly if close to the water source term, concluding that the application interest for such investigations is more practical than it might seem at first glance; on the other hand, the advantage of handling just linear systems is therein highlighted. More recently, in Basha (1999), the steady solution is derived using perturbation expansions methods, with a possibly nonzero water extraction term: as in other papers (see for instance Ursino 2000), the solution is represented as the superposition of the terms: the zero-order part, which is the linear solution, and the first-order correction term, which accounts for the nonlinearity. This concept is also reported and generalized in Severino and Tartakovsky (2014), claiming that "flow in both root systems and ambient soils can be represented by a sequence of steady states": also the aforementioned paper makes use of matched asymptotic expansions for steady flows, relaxing or eliminating classical previous assumptions (infinite soil column and constant hydraulic head prescribed on its surface).…”

Section: Introduction To the Physical Problemmentioning

confidence: 99%

Optimizing Water Consumption in Richards’ Equation Framework with Step-Wise Root Water Uptake: A Simplified Model

et al. 2022

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This work arises from the need of exploring new features for modeling and optimizing water consumption in irrigation processes. In particular, we focus on water flow model in unsaturated soils, accounting also for a root water uptake term, which is assumed to be discontinuos in the state variable. We investigate the possibility of accomplishing such optimization by computing the steady solutions of a $$\theta$$ θ -based Richards equation revised as equilibrium points of the ODEs system resulting from a numerical semi-dicretization in the space; after such semi-discretization, these equilibrium points are computed exactly as the solutions of a linear system of algebraic equations: the case in which the equilibrium lies on the threshold for the uptake term is of particular interest, since the system considerably simplifies. In this framework, the problem of minimizing the water waste below the root level is investigated. Numerical simulations are provided for representing the obtained results. Article Highlights Root water uptake is modelled in a Richards’ equation framework with a discontinuous sink term. After a proper semidiscretization in space, equilibrium points of the resulting nonlinear ODE system are computed exactly. The proposed approach simplifies a control problem for optimizing water consumption.

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