MATHEMATICAL MODELLING OF THE DYNAMICS OF GROUNDWATER LEVEL VARIATIONS
DOI:
https://doi.org/10.47390/ts-v4i3y2026N06Keywords:
groundwater, groundwater level dynamics, mathematical modelling, filtration process, analytical solution.Abstract
Understanding the mechanisms governing groundwater level variations is of considerable scientific importance for analysing the formation and development of hydrogeological systems. The movement of groundwater represents a complex hydrodynamic process influenced by both natural conditions and anthropogenic factors. Determining its spatial and temporal behaviour is therefore essential for the rational utilisation of water resources and the efficient management of reclamation and drainage systems. In this context, the present study focuses on the mathematical modelling of groundwater level dynamics. Within the framework of the research, a mathematical model describing the temporal evolution of groundwater levels along the OX spatial direction has been developed. The model is formulated on the basis of a differential equation representing the filtration process and is supplemented with appropriate initial and boundary conditions. To obtain an analytical solution, the Fourier series method is employed. As a result, the general solution describing groundwater level variations as a function of spatial coordinate and time is derived in the form of a series consisting of trigonometric functions multiplied by exponential terms. The obtained analytical representation makes it possible to investigate the distribution patterns of groundwater levels along the OX direction and to analyse the stabilisation behaviour of hydrodynamic processes over time. The modelling results indicate that the filtration coefficient, hydraulic gradient, physical properties of the porous medium, and geometric parameters of the aquifer layer act as the principal factors governing groundwater dynamics. The proposed mathematical approach can be applied to the theoretical analysis of groundwater level variations, to the investigation of hydrogeological system evolution, and to the prediction of water resource conditions. The scientific novelty of the study lies in deriving an analytical solution for groundwater dynamics through one-dimensional mathematical modelling and in identifying the fundamental regularities of hydrogeological processes.
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