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Open AccessArticle

A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

1
LISAC, Université Sidi Mohamed Ben Abdellah, Faculté des Sciences (Dhar El Mehraz), Fès 30003, Morocco
2
LMAP, Universite de Pau et des Pays de l’Adour, CNRS, E2S UPPA, 64000 Pau, France
3
L2M3S-ENSAM, Université Moulay Ismaïl, Meknès 50000, Morocco
*
Author to whom correspondence should be addressed.
Water 2020, 12(6), 1639; https://doi.org/10.3390/w12061639
Received: 21 April 2020 / Revised: 25 May 2020 / Accepted: 29 May 2020 / Published: 8 June 2020
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 X . 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. View Full-Text
Keywords: saltwater intrusion; sharp interface; finite volume; DuMuX; porous media; heterogeneity saltwater intrusion; sharp interface; finite volume; DuMuX; porous media; heterogeneity
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MDPI and ACS Style

Aharmouch, A.; Amaziane, B.; El Ossmani, M.; Talali, K. A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers. Water 2020, 12, 1639.

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