An Analytical Solution to the 1D Drainage Problem

Konstantinos Kalimeris and Leonidas Mindrinos ()
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Konstantinos Kalimeris: Mathematics Research Center, Academy of Athens, 10679 Athens, Greece
Leonidas Mindrinos: Department of Natural Resources Development and Agricultural Engineering, Agricultural University of Athens, 11855 Athens, Greece

Mathematics, 2025, vol. 13, issue 20, 1-11

Abstract: We derive an analytical solution to the one-dimensional linearized Boussinesq equation with mixed boundary conditions (Dirichlet–Neumann), formulated to describe drainage in porous media. The solution is obtained via the unified transform method (Fokas method), extending its previous applications in infiltration problems and illustrating its utility in soil hydrology. An explicit integral representation is constructed, considering different types of initial conditions. Numerical examples are presented to demonstrate the accuracy of the solution, with direct comparisons to the classical Fourier series approach.

Keywords: drainage problem; Fokas method; unified transform; integral solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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