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

• 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
• ISSN: 1431-2174; 1435-0157
• DOI: 10.1007/s10040-014-1102-8

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.