A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers
We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of nat...
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MDPI AG
2020-06-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/12/6/1639 |
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| author | Abdelkrim Aharmouch Brahim Amaziane Mustapha El Ossmani Khadija Talali |
| author_facet | Abdelkrim Aharmouch Brahim Amaziane Mustapha El Ossmani Khadija Talali |
| author_sort | Abdelkrim Aharmouch |
| collection | DOAJ |
| description | We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mi>X</mi> </msup> </semantics> </math> </inline-formula>. The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method. |
| first_indexed | 2024-03-10T19:19:18Z |
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| id | doaj.art-ce0d1a343f244c9da47c6db3f0993c73 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T19:19:18Z |
| publishDate | 2020-06-01 |
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| spelling | doaj.art-ce0d1a343f244c9da47c6db3f0993c732023-11-20T03:09:50ZengMDPI AGWater2073-44412020-06-01126163910.3390/w12061639A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal AquifersAbdelkrim Aharmouch0Brahim Amaziane1Mustapha El Ossmani2Khadija Talali3LISAC, Université Sidi Mohamed Ben Abdellah, Faculté des Sciences (Dhar El Mehraz), Fès 30003, MoroccoLMAP, Universite de Pau et des Pays de l’Adour, CNRS, E2S UPPA, 64000 Pau, FranceL2M3S-ENSAM, Université Moulay Ismaïl, Meknès 50000, MoroccoL2M3S-ENSAM, Université Moulay Ismaïl, Meknès 50000, MoroccoWe present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mi>X</mi> </msup> </semantics> </math> </inline-formula>. The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.https://www.mdpi.com/2073-4441/12/6/1639saltwater intrusionsharp interfacefinite volumeDuMu<sup><i>X</i></sup>porous mediaheterogeneity |
| spellingShingle | Abdelkrim Aharmouch Brahim Amaziane Mustapha El Ossmani Khadija Talali A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers Water saltwater intrusion sharp interface finite volume DuMu<sup><i>X</i></sup> porous media heterogeneity |
| title | A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers |
| title_full | A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers |
| title_fullStr | A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers |
| title_full_unstemmed | A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers |
| title_short | A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers |
| title_sort | fully implicit finite volume scheme for a seawater intrusion problem in coastal aquifers |
| topic | saltwater intrusion sharp interface finite volume DuMu<sup><i>X</i></sup> porous media heterogeneity |
| url | https://www.mdpi.com/2073-4441/12/6/1639 |
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