Numerical Modeling of Nonlinear Groundwater Flow in a Heterogeneous Four-Layer Porous Medium

Abstract

Abstract

This paper presents a comprehensive numerical modeling of nonlinear groundwater flow in a synthetic heterogeneous four-layer porous medium. Multilayered aquifer systems present significant modeling challenges due to nonlinear filtration and interlayer exchange processes. The mathematical model consists of four coupled nonlinear parabolic partial differential equations, where the nonlinearity arises from the dependence of hydraulic conductivity on hydraulic head. Vertical exchange between layers is described by Darcy’s law through separating aquicludes. The system is solved using a fully implicit finite-difference scheme by employing an alternating-direction implicit approach, resulting in a block-tridiagonal system of equations. The model is verified using analytical solutions and mass conservation tests. Application to a synthetic aquifer system demonstrates the model’s ability to reproduce complex transient behavior, including delayed response of upper layers to pumping and asymmetry of water-level drawdown cones due to nonlinear conductivity. The model’s greatest sensitivity is observed to the conductivity of the pumped layer and the vertical conductivity of the separating layers. The proposed approach represents a robust tool for groundwater management in structurally complex geological settings.