Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations
In gravity irrigation, how water is distributed in the soil profile makes it necessary to study and develop methodologies to model the process of water infiltration and redistribution. In this work, a model is shown to simulate the advancing front in border irrigation based on the one dimensional eq...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1039 |
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| author | Sebastián Fuentes Carlos Fuentes Heber Saucedo Carlos Chávez |
| author_facet | Sebastián Fuentes Carlos Fuentes Heber Saucedo Carlos Chávez |
| author_sort | Sebastián Fuentes |
| collection | DOAJ |
| description | In gravity irrigation, how water is distributed in the soil profile makes it necessary to study and develop methodologies to model the process of water infiltration and redistribution. In this work, a model is shown to simulate the advancing front in border irrigation based on the one dimensional equations of Barré de Saint-Venant for the surface flow and the equation of Green and Ampt for the flow in a porous medium. The solutions were obtained numerically using a finite difference Lagrangian scheme for the surface flow and the Raphson method for the subsurface flow. The model was validated with data obtained from the literature from an irrigation test and its predictive capacity was compared with another model and showed excellent results. The hydrodynamic parameters of the soil, necessary to obtain the optimal irrigation discharge, were obtained through the solution of the inverse problem using the Levenberg–Marquardt optimization algorithm. Finally, the results found here allow us to recommend that this model be used to design and model border irrigation, since the infiltration equation uses characteristic parameters of the physical soil. |
| first_indexed | 2024-03-09T11:38:56Z |
| format | Article |
| id | doaj.art-274540e40f1d468a91525a993bed4ef9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:56Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-274540e40f1d468a91525a993bed4ef92023-11-30T23:36:17ZengMDPI AGMathematics2227-73902022-03-01107103910.3390/math10071039Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt EquationsSebastián Fuentes0Carlos Fuentes1Heber Saucedo2Carlos Chávez3Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Cerro de las Campanas SN, Col. Las Campanas, Queretaro 76010, MexicoMexican Institute of Water Technology, Paseo Cuauhnáhuac Num. 8532, Jiutepec, Morelos 62550, MexicoNational Water Commission, Avenida Insurgentes Sur Num. 2416, Copilco el Bajo, Ciudad de Mexico 04340, MexicoWater Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Cerro de las Campanas SN, Col. Las Campanas, Queretaro 76010, MexicoIn gravity irrigation, how water is distributed in the soil profile makes it necessary to study and develop methodologies to model the process of water infiltration and redistribution. In this work, a model is shown to simulate the advancing front in border irrigation based on the one dimensional equations of Barré de Saint-Venant for the surface flow and the equation of Green and Ampt for the flow in a porous medium. The solutions were obtained numerically using a finite difference Lagrangian scheme for the surface flow and the Raphson method for the subsurface flow. The model was validated with data obtained from the literature from an irrigation test and its predictive capacity was compared with another model and showed excellent results. The hydrodynamic parameters of the soil, necessary to obtain the optimal irrigation discharge, were obtained through the solution of the inverse problem using the Levenberg–Marquardt optimization algorithm. Finally, the results found here allow us to recommend that this model be used to design and model border irrigation, since the infiltration equation uses characteristic parameters of the physical soil.https://www.mdpi.com/2227-7390/10/7/1039hydrodynamic wave modelfinite differenceimplicit schemesurface flowsubsurface flow |
| spellingShingle | Sebastián Fuentes Carlos Fuentes Heber Saucedo Carlos Chávez Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations Mathematics hydrodynamic wave model finite difference implicit scheme surface flow subsurface flow |
| title | Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations |
| title_full | Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations |
| title_fullStr | Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations |
| title_full_unstemmed | Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations |
| title_short | Border Irrigation Modeling with the Barré de Saint-Venant and Green and Ampt Equations |
| title_sort | border irrigation modeling with the barre de saint venant and green and ampt equations |
| topic | hydrodynamic wave model finite difference implicit scheme surface flow subsurface flow |
| url | https://www.mdpi.com/2227-7390/10/7/1039 |
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