Article · Mathematics · January 9, 2026
A Nonlinear Model of Three-Layer Groundwater Flow with Evaporation Dependent on the Critical Groundwater Level
Abdinabi Mukhamadiyev, Marat Karimov, Toshtemir Abdikhafizovich Khujakulov, Otabek Sattarov, JinSoo Cho
Abstract
A nonlinear mathematical model is developed for unsteady groundwater flow in a three-layer heterogeneous aquifer system, comprising a confined aquifer, a covering layer, and a weakly permeable barrier. The model incorporates infiltration and evaporation governed by the M.M. Krylov–S.F. Averyanov law, where evaporation intensity depends on a critical groundwater level. Governing equations are nondimensionalized and solved using the alternating direction implicit (ADI) method with quasi-linearization to treat nonlinearities. Periodic variations in precipitation and evaporation are considered, alongside variable boundary permeabilities. The approach enables realistic simulation of multi-layer aquifer dynamics under diverse climatic and hydrogeological conditions, offering a robust tool for sustainable groundwater management, drought risk assessment, and aquifer protection strategies.
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