Modeling of the process of unsteady filtration of groundwater with a free surface taking into account infiltration flows
DOI:
https://doi.org/10.71310/pcam.4_74.2026.05Keywords:
mathematical model, numerical algorithm, groundwater, computational experiments, hydrodynamic parameters, infiltration frontAbstract
A nonlinear mathematical model with boundary, initial and internal conditions is proposed for monitoring and forecasting unsteady groundwater seepage with a free surface, taking into account infiltration flows and the hydrodynamic parameters of the soil. To determine the main factors directly influencing groundwater level changes over time, a minimizing functional is presented, which allows one to determine the ranges of the significant parameters in which they substantially influence the infiltration process. The problem is solved numerically by the locally one-dimensional scheme of A. A. Samarskii; numerical experiments on model problems showed that the best results are achieved by applying the principle of symmetrization. A model problem for a symmetric domain with a square boundary and a square infiltration region was solved. Analysis of the results showed that, for a constant seepage coefficient, the infiltration front propagates absolutely symmetrically over time within the seepage domain, as expected from physical considerations. It was established that the locally one-dimensional scheme is effective for this class of problems, can be successfully applied in combination with the symmetrization method and can be recommended for solving problems of modeling and forecasting the groundwater regime.
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