Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13203279
Institutions: Academy of Athens, Agricultural University of Athens
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4415147616