Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer
The solution to the second-order fuzzy unsteady nonlinear partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite, unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level...
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MDPI AG
2023-04-01
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| Series: | Environmental Sciences Proceedings |
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| Online Access: | https://www.mdpi.com/2673-4931/25/1/70 |
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| author | Christos Tzimopoulos Nikiforos Samarinas Kyriakos Papadopoulos Christos Evangelides |
| author_facet | Christos Tzimopoulos Nikiforos Samarinas Kyriakos Papadopoulos Christos Evangelides |
| author_sort | Christos Tzimopoulos |
| collection | DOAJ |
| description | The solution to the second-order fuzzy unsteady nonlinear partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite, unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level of the lake; thus, the aquifer is recharging from the lake. The fuzzy solution is presented by a simple algebraic equation transformed in a fourth-degree polynomial approximation for the head profiles. In order to solve this equation, the initial and boundary conditions, as well as the numerous soil properties, must be known. A fuzzy approach is used to solve the problem since the aforementioned auxiliary conditions are vulnerable to various types of uncertainty resulting from human and machine errors. The physical problem described by a partial differential equation and the generalized Hukuhara derivative and the application of this theory for the partial derivatives were chosen as solving methods. In order to evaluate the accuracy and effectiveness of the suggested fuzzy analytical method, this study compares the findings of fuzzy analysis to those obtained using the Runge–Kutta method. This comparison attests to the accuracy of the former. Additionally, this results in a fuzzy number for water level profiles as well as for the water volume variation, whose α-cuts, provide according to Possibility Theory, the water levels and the water volume confidence intervals with probability <i>p</i> = 1 − α. |
| first_indexed | 2024-03-11T02:30:14Z |
| format | Article |
| id | doaj.art-f236e3a71639475ca0aefd9ae915d584 |
| institution | Directory Open Access Journal |
| issn | 2673-4931 |
| language | English |
| last_indexed | 2024-03-11T02:30:14Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Environmental Sciences Proceedings |
| spelling | doaj.art-f236e3a71639475ca0aefd9ae915d5842023-11-18T10:19:57ZengMDPI AGEnvironmental Sciences Proceedings2673-49312023-04-012517010.3390/ECWS-7-14303Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined AquiferChristos Tzimopoulos0Nikiforos Samarinas1Kyriakos Papadopoulos2Christos Evangelides3Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceDepartment of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceDepartment of Mathematics, Kuwait University—Khaldiya Campus, Safat 13060, KuwaitDepartment of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceThe solution to the second-order fuzzy unsteady nonlinear partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite, unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level of the lake; thus, the aquifer is recharging from the lake. The fuzzy solution is presented by a simple algebraic equation transformed in a fourth-degree polynomial approximation for the head profiles. In order to solve this equation, the initial and boundary conditions, as well as the numerous soil properties, must be known. A fuzzy approach is used to solve the problem since the aforementioned auxiliary conditions are vulnerable to various types of uncertainty resulting from human and machine errors. The physical problem described by a partial differential equation and the generalized Hukuhara derivative and the application of this theory for the partial derivatives were chosen as solving methods. In order to evaluate the accuracy and effectiveness of the suggested fuzzy analytical method, this study compares the findings of fuzzy analysis to those obtained using the Runge–Kutta method. This comparison attests to the accuracy of the former. Additionally, this results in a fuzzy number for water level profiles as well as for the water volume variation, whose α-cuts, provide according to Possibility Theory, the water levels and the water volume confidence intervals with probability <i>p</i> = 1 − α.https://www.mdpi.com/2673-4931/25/1/70unsteady flowfuzzy partial derivativesnumerical methods |
| spellingShingle | Christos Tzimopoulos Nikiforos Samarinas Kyriakos Papadopoulos Christos Evangelides Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer Environmental Sciences Proceedings unsteady flow fuzzy partial derivatives numerical methods |
| title | Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer |
| title_full | Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer |
| title_fullStr | Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer |
| title_full_unstemmed | Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer |
| title_short | Fuzzy Analytical Solution for the Case of a Semi-Infinite Unconfined Aquifer |
| title_sort | fuzzy analytical solution for the case of a semi infinite unconfined aquifer |
| topic | unsteady flow fuzzy partial derivatives numerical methods |
| url | https://www.mdpi.com/2673-4931/25/1/70 |
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