MATHEMATICAL MODEL OF GROUNDWATER LEVEL DYNAMICS AND SALT MIGRATION IN A POROUS MEDIUM
DOI:
https://doi.org/10.47390/ts-v4i4y2026N06Keywords:
groundwater, groundwater level dynamics, mathematical modelling, filtration processes, analytical solution.Abstract
This paper investigates the mathematical modelling of groundwater level variations and the transport of salt concentration within porous media. The filtration behaviour of groundwater is described based on the Dupuit–Forchheimer assumption, while the governing equation for groundwater level dynamics is derived from the law of mass conservation, resulting in a nonlinear differential equation of the Boussinesq type. In addition, the migration of dissolved salts within the porous medium is represented through a convection–diffusion equation. During the salt transport process, the filtration velocity is determined by the groundwater discharge, and the interdependence between groundwater level and salt concentration is incorporated into the formulation. As a result, a coupled mathematical model describing both groundwater level fluctuations and salt concentration dynamics has been developed. Appropriate initial and boundary conditions are specified for the proposed model, and the physical interpretation of the governing processes is discussed. The developed model provides a framework for analysing the hydrodynamic regime of groundwater and the spatial–temporal distribution patterns of salt transport in porous media. Furthermore, the proposed approach can be applied to evaluate groundwater level changes in irrigated regions, to predict soil salinisation processes, and to support the rational management of water resources.
References
1. Qian Y., Zhu Y., Zhang X., Wu J., Ye M., Mao W., Wu J., Huang J., Yang J. A local grid-refined numerical groundwater model based on the vertex-centred finite-volume method // Advances in Water Resources. – 2023. – DOI: 10.1016/j.advwatres.2023.104392.
2. Remson I. Introduction to groundwater modeling: finite difference and finite element methods // Eos, Transactions American Geophysical Union. – 1982. – Vol. 63. – P. 778. – DOI: 10.1029/EO063i037p00778-02.
3. Santoso H., Situmorang R. Groundwater modeling in open pit coal mining plans using the finite difference method // IOP Conference Series: Earth and Environmental Science. – 2025. – Vol. 1517. – Art. 012025. – DOI: 10.1088/1755-1315/1517/1/012025.
4. Sbai M., Larabi A. A deforming mixed-hybrid finite element model for robust groundwater flow simulation in 3D unconfined aquifers with unstructured layered grids // Water. – 2023. – DOI: 10.3390/w15061177.
5. Shittu M., Usman M. Mathematical modeling of transient and steady-state groundwater flow in a confined aquifer // Journal of Applied Sciences and Environmental Management. – 2024. – DOI: 10.4314/jasem.v28i3.15.
6. Singh K., Pathania T. Development and real field application of meshless generalized finite difference method for unconfined groundwater flow modelling // Mathematics and Computers in Simulation. – 2025. – Vol. 240. – P. 332–346. – DOI: 10.1016/j.matcom.2025.07.027.
7. Strack O. Finite differences and finite elements // Groundwater Mechanics. – Cambridge: Cambridge University Press, 2017. – P. 403–422. – DOI: 10.1017/9781316563144.011.
8. Tanbay T., Durmayaz A. Numerical modelling of groundwater radionuclide transport with finite difference-based method of lines // Journal of Radioanalytical and Nuclear Chemistry. – 2023. – Vol. 332. – P. 4833–4845. – DOI: 10.1007/s10967-023-09020-1.
9. Daliev S., Urakov S., Sirojiddinov F., Abbasova M., Nurboboev S. Three-Dimensional Mathematical Model of the Process of Groundwater Level Change // IAENG International Journal of Applied Mathematics. – 2025. – Vol. 55, No. 11.
10. Daliev S., Urakov S., Elmurodov U., Xaitov O., Abbasova M. A Three-Dimensional Mathematical Model for Groundwater Level Variations in a Two-Layered Medium // Engineering, Technology & Applied Science Research. – 2025. – Vol. 15, No. 5. – P. 28368–28376.
11. Daliev S., Xudoyberdiyev S., Abdullayeva Z., Shikhnazarova G. Three-dimensional mathematical model of groundwater level and salt concentration changes in a single-layer media // AIP Conference Proceedings. – 2024. – Vol. 3045, No. 1. – Article 050014.
12. Daliev S., Kurbonov N., Ibragimova K., Dzhurayeva S. Numerical modeling of groundwater level changes in multilayer media // AIP Conference Proceedings. – 2024. – Vol. 3045, No. 1. – Article 040025.
13. Daliev S., Sirojiddinov F., Khaitov O. Developing mathematical models to study changes in groundwater levels and salt concentration // E3S Web of Conferences. – 2024. – Vol. 589. – Article 03011.
This work is licensed under a 