Fourier series solution for an anisotropic and layered configuration of the dispersive Henry Problem

B. Koohbor, M. Fahs, B. Belfort, B. Ataie-Ashtiani, C. T. Simmons

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Henry Problem (HP) still plays an important role in benchmarking numerical models of seawater intrusion (SWI) as well as being applied to practical and managerial purposes. The popularity of this problem is due to having a closed-form semi-analytical (SA) solution. The early SA solutions obtained for HP were limited to extensive assumptions that restrict its application in practical works. Several further studies expended the generality of the solution by assuming lower diffusion coefficients or including velocity-dependent dispersion in the results. However, all these studies are limited to homogeneous and isotropic domains. The present work made an attempt to improve the reality of the SA solution obtained for dispersive HP by considering anisotropic and stratified heterogeneous coastal aquifers. The solution is obtained by defining Fourier series for both stream function and salt concentration, applying a Galerkin treatment using the Fourier modes as trial functions and solving the flow and the salt transport equations simultaneously in the spectral space. In order to include stratified heterogeneity, a special depth-hydraulic conductivity model is applied that can be solved analytically without significant mathematical complexity. Several examples are proposed and studied. The results show excellent agreement between the SA and numerical solutions obtained with an in-house advanced finite element code.

Original languageEnglish
Article number00014
JournalE3S Web of Conferences
Publication statusPublished - 17 Sept 2018
Event25th Salt Water Intrusion Meeting, SWIM 2018 - Gdansk, Poland
Duration: 17 Jun 201822 Jun 2018

Bibliographical note

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0 (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


  • Fourier series
  • Henry problem
  • Semi-analytical solution
  • Stratified heterogeneity
  • Velocity-dependent dispersion


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