Journal of Aquifer and Qanat
In collaboration Iranian Hydraulic Association

Providing A Semi-Analytical Solution To The Henry Problem and The Effect of Bed Slope on Seawater Intrusion into Confined Coastal Aquifers

Document Type : Original Article

Authors

saleh mehdizadeh 1
Rasoul Mir abbasi najaf abadi 1
ali Raeisi Isa-Abadi 1
Marwan Fahs 2

1 Department of Water Engineering, Shahrekord University, Shahrekord, Iran.

2 Laboratoire d’Hydrologie de Géochimie, National School for Water and Environmental Engineering, University of Strasbourg, France.

10.22077/jaaq.2026.10702.1136
Abstract
In this study, a semi-analytical solution to the Henry problem in sloping coastal aquifers is developed. Using the Fourier–Galerkin method, the governing equations of variable-density flow and mass transport under steady-state conditions for a sloping geometry are solved, and the Fourier series coefficients are determined using Newton’s method along with analytical calculation of the Jacobian. The main objective of this study is to verify the validity of the proposed semi-analytical solution in non-horizontal geometries and to investigate the effect of bed slope on the advancement of the saltwater wedge into the aquifer. Comparison between the semi-analytical solution and the numerical results obtained from the COMSOL model indicates a high degree of overlap among the 25%, 50%, and 75% isochlor lines, confirming the accuracy and stability of the proposed method. Results for slopes ranging from −30° to +30° show that a landward slope increases the length of saltwater intrusion, whereas a seaward slope compresses the wedge and reduces its advance. The semi-analytical solution developed in this study can be used as a reliable benchmark for evaluating the performance of numerical models and as a powerful tool for analyzing management scenarios and assessing the impacts of climate change in inclined coastal aquifers.

Keywords

Inclined coastal aquifers
Henry Problem
Semi-Analytical solution
Saltwater intrusion
COMSOL model
Subjects
Journal of Aquifer and Qanat
Volume 7, Issue 1
August 2026
Pages 1-24

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