A numerical procedure for geochemical compaction in the presence of discontinuous reactions

Agosti, Abramo; Giovanardi, Bianca; Formaggia, Luca; Scotti, Anna

doi:10.1016/j.advwatres.2016.06.001

Cited by 10 publications

(11 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…function which takes values in the interval [0, i ] ; in particular, for any time t and any depth z ∈ (z i−1 , z i ] with i ∈ {1, … , N − 1} such that 𝜃(t, z) = θi equation ( 5) reads as On the other hand, the discontinuity in (8) suggests to study equation ( 5) as a discontinuous differential equation using Filippov theory, in the frame of Agosti et al (2016), Agosti et al (2015), , where novel numerical techniques have been proposed; nevertheless, this treatise goes beyond the goals of our work.…”

Section: The Proposed Modelmentioning

confidence: 99%

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

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Section: The Proposed Modelmentioning

confidence: 99%

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

et al. 2022

View full text Add to dashboard Cite

show abstract

“…It should be observed that the width of the sliding region increases as the absolute value of the parameter F increases. 4. Sets of attraction of crossing/sliding regions.…”

Section: Example (Seementioning

confidence: 99%

“…pred (a) Computation of the predictions. which we have chosen the increment to be h = 3 √ eps, where eps is the machine precision;…”

Section: 2mentioning

confidence: 99%

“…Examples include mechanical, robotic, electrical, biological, climate, and even financial models (see for instance [12,18,23,38,39]). Recently, standard techniques to study discontinuous systems of ODEs have been employed in the simulation of reaction diffusion systems with discontinuous forcing terms (see for instance [4,2,3]). The solutions of such systems can be simulated using suitable numerical methods, see for instance the book [1] or the papers [10,11,37].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems

Colombo¹,

Buono²,

Lopez³

et al. 2018

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

Several models in the applied sciences are characterized by instantaneous changes in the solutions or discontinuities in the vector field. Knowledge of the geometry of interaction of the flow with the discontinuities can give new insights on the behaviour of such systems. Here, we focus on the class of the piecewise smooth systems of Filippov type. We describe some numerical techniques to locate crossing and sliding regions on the discontinuity surface, to compute the sets of attraction of these regions together with the mathematical form of the separatrices of such sets. Some numerical tests will illustrate our approach.

show abstract

“…This approach represents the main novelty of the paper. We have to notice that Filippov theory has also been used in the numerical solution of geosciences and geochemical models but only to treat discontinuities in time (see [21], [22]).…”

Section: Introduction To the Physical Problemmentioning

confidence: 99%

The 1D Richards’ equation in two layered soils: a Filippov approach to treat discontinuities

Berardi

Difonzo

Vurro

et al. 2018

Advances in Water Resources

View full text Add to dashboard Cite

A numerical procedure for geochemical compaction in the presence of discontinuous reactions

Cited by 10 publications

References 22 publications

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

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

Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems

The 1D Richards’ equation in two layered soils: a Filippov approach to treat discontinuities

Contact Info

Product

Resources

About