Mathematical Modeling and Numerical Solutions of the Unsteady Filtration Problem of Groundwater

Abstract

This study explores the complex dynamics of unsteady groundwater filtration, a pivotal aspect of sustainable water management in arid regions. Utilizing a novel mathematical model, the research simulates groundwater movement in heterogeneous, multilayered aquifers, a common scenario in Central Asia's agriculture-dominated landscapes. The model integrates the Myatiev-Girinsky hypothesis with a system of partial differential equations, capturing the intricate interplay of various factors like infiltration, evaporation, and hydraulic structure operations. A significant innovation of this work is the application of the finite difference method, combined with dimensionless variables, to solve the boundary problem. This approach not only enhances model accuracy but also broadens its applicability to real-world scenarios. The findings offer crucial insights for effective groundwater management, particularly in regions where agriculture heavily depends on artificial irrigation. This research contributes significantly to the fields of environmental hydraulics and water resource management, presenting a valuable tool for both theoretical analysis and practical application in managing vital water resources.