We present an approach for solving problems of saltwater intrusion in aquifers with an hydraulic conductivity that varies in the vertical direction. The approach is based on the concept of a comprehensive potential, whose gradient exactly represents the vertically integrated discharge, which is, by definition, a two-dimensional vector. We apply the approach to an island in Sweden and use it to estimate maximum allowable pumping rates of wells that recover part of the infiltration on the island.
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The source code of the MATLAB program is provided as supporting information to this paper. The authors are grateful to Anvar Kacimov, who suggested a function for the vertically varying hydraulic conductivity that resulted in a major improvement of the application reported in this paper, and can be obtained online (https://github.com/eriktoller/interface_flow_with_vertically_varying_hydraulic_conductivity). The authors thank Randal Barnes, Philippe LeGrand, R. William Olsen, Bonnie Ausk, and Taha Namazi for their helpful comments during presentations of this?work.
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- analytic element method
- element strings
- groundwater flow
- lakes and rivers
- line elements
- vertically integrated flow