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  4. Numerical solution of the vertical infiltration problem in bounded profiles

Numerical solution of the vertical infiltration problem in bounded profiles

MMC.
2025;
Volume 12, Number 1
: pp. 83–89
https://doi.org/10.23939/mmc2025.01.083
Received: May 16, 2024
Accepted: September 26, 2024

Borachok I., Chapko R., Mindrinos L.  Numerical solution of the vertical infiltration problem in bounded profiles.  Mathematical Modeling and Computing. Vol. 12, No. 1, pp. 83–89 (2025)

Authors:
  1. I. Borachok
  2. R. Chapko
  3. L. Mindrinos
1
Ivan Franko National University of Lviv
2
Ivan Franko National University of Lviv
3
Agricultural University of Athens

There is presented a numerical solution of the one-dimensional infiltration problem in bounded profiles.  The soil is assumed to have constant water diffusivity and linear dependence between the hydraulic conductivity and the water content.  Then, the vertical infiltration problem is modeled as an initial boundary value problem for a diffusion equation.  We combine the finite difference scheme for the time variable with the fundamental sequence method for the spatial variable.  The derived numerical scheme is applied to both flooding and rainfall scenarios.  The convergence of the numerical approximated solution to the analytical one justifies the applicability of the method.

advection-dispersion equation
Rothe's method
fundamental sequences method
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