A semi-analytical solution for saltwater intrusion with a very narrow transition zone

The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b  = 0.1). Fin...

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Bibliographic Details
Published in:Hydrogeology journal 2014-03, Vol.22 (2), p.501-506
Main Authors: Younes, Anis, Fahs, Marwan
Format: Article
Language:English
Subjects:
Algorithms
Aquatic Pollution
Aquifers
Benchmarking
Coasts
Density
Dynamical systems
Earth and Environmental Science
Earth Sciences
Fresh water
Geology
Geophysics/Geodesy
Groundwater flow
Hydrogeology
Hydrology
Hydrology/Water Resources
Intrusion
Jacobians
Mathematical models
Nonlinear dynamics
Saline water
Saline water intrusion
Technical Note
Transition zone
Waste Water Technology
Water Management
Water Pollution Control
Water Quality/Water Pollution
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Summary:The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b  = 0.1). Finding a stable semi-analytical solution for small values of b is challenging due to the low convergence of the corresponding nonlinear system. In this work, an accurate semi-analytical solution is developed in the case of a very narrow transition zone corresponding to b  = 0.005. About 6,330 terms are used in the Fourier series to accurately represent the solution. The resolution of the corresponding highly nonlinear system is made possible by the modified Powell hybrid algorithm due to the analytical evaluation of the Jacobian, which drastically reduces the computational time. The new test problem is also investigated numerically using different numerical methods and different mesh sizes to show its high worthiness, compared to the standard Henry problem, for benchmarking density driven flow codes.
ISSN:1431-2174
1435-0157
DOI:10.1007/s10040-014-1102-8