Modeling of groundwater flow in a multilayer porous medium based on a nonlinear mathematical model

In the present study, a nonlinear mathematical model has been developed to describe the unsteady groundwater flow in a three-layer heterogeneous porous medium with arbitrary boundary conditions. The model includes an upper layer, a highly permeable main layer, and a low-permeability bottom layer. The vertical flow from a well, evaporation, and infiltration processes have been analyzed within the modeling framework. The evaporation process has been modeled using the M.M. Krylov–S.F. Averyanov law, while the behavior of the low-permeability layer has been studied based on M.S. Hantush’s theory. A finite difference discretization scheme using a quasi-linear iterative approach has been proposed to solve the nonlinear terms. Dimensionless parameters have been introduced and used to normalize the model equations. The model has been formulated using initial conditions and third-type boundary conditions. Numerical results have been presented, showing the time-dependent distribution of water table elevation and interlayer vertical flow velocity. The modeling approach has been substantiated as numerically stable and computationally efficient. Overall, the study offers a robust methodology for predicting and managing groundwater flow in multilayer porous systems.

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