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Mathematical Modeling of Filtration and Geomigration Under Conditions of Anthropogenic Load
(Український державний університет науки і технологій, Дніпро, 2025) Bubnova, Olena A.; Miroshnik, Vitaliy A.; Markul, Ruslan V.; Mashykhina, Polina B.; Tatarko, Larysa H.
ENG: Purpose. The aim of this study is to develop mathematical models for predicting the processes of contamination of the aeration zone and groundwater in the event of leachate leakage from a solid waste landfill. The mathematical models take into account typical hydrological parameters: porosity of the aeration zone, aquifer, filtration coefficient of the aeration zone, filtration coefficient of the underground aquifer, intensity of leachate infiltration into the aeration zone and underground aquifer. Methodology. A one-dimensional filtration equation and a one-dimensional mass transfer equation were used to model the process of infiltrate migration in the aeration zone. The modeling of the process of contamination of the underground aquifer, which receives infiltrate from the landfill, was carried out on the basis of a two-dimensional equation (planned model) of geomigration. For the numerical integration of the model equations, a variable-triangular finite-difference splitting scheme was used. The numerical integration of the two-dimensional geomigration equation is performed using the splitting scheme. The peculiarity of the proposed numerical models is that the value of the unknown function can be determined by an explicit formula. Findings. Numerical models have been developed to solve the complex problem of predicting the contamination of the aeration zone and underground flow in the case of infiltration of an impurity from a solid waste landfill. Originality. Numerical models of filtration and mass transfer of impurities in the case of migration of infiltrate from a municipal solid waste landfill through the aeration zone and into groundwater are proposed. To apply these mathematical models, standard hydrological information is required. The models are aimed at solving complex problems in the field of environmental safety and protection. They make it possible to determine the negative impact of landfills on the environment at the stage of justifying the location of future landfills and their size. Practical value. The proposed mathematical models use standard hydrological information, which is important for serial calculations in design organizations, and can be useful for assessing the impact of landfills on environmental pollution.
Modeling the Dynamics of Groundwater in Applied Problems
(ESI “Prydniprovska State Academy of Civil Engineering and Architecture”, USUST, Dnipro, 2025) Tiutkin, Oleksii L.; Bubnova, Olena A.; Markul, Ruslan V.; Miroshnyk, Vitalii A.; Mashykhina, Polina B.
ENG: Problem statement. Forecasting and analyzing groundwater dynamics under anthropogenic impact on aquifers is a pressing issue. This task arises when designing drainage systems for flooded areas, designing water intakes from underground sources, the impact of waste disposal sites on the movement of groundwater, and water leakage from water supply and sewage systems. Anthropogenic impact can affect both groundwater (unconfined aquifers) and confined aquifers. Technogenic impact can occur through a system of wells, leakage of effluents from landfills, infiltration of precipitation, and irrational irrigation. Solving this type of problem requires the use of multifactorial filtration models. The purpose of the article. To conduct a comprehensive analysis of mathematical models in groundwater dynamics problems and to identify their advantages and disadvantages. Conclusions. The analysis showed that the modern approach to solving groundwater dynamics problems is to use multidimensional filtration equations that take into account changes in the groundwater level (or hydrodynamic pressure in the confined aquifer) over time. These modeling equations take into account water infiltration into underground horizons. The boundary conditions of the modeling filtration equations that ensure the correct formulation of the boundary problem are considered. It is shown that the formulation of specific groundwater dynamics problems (drainage, operation of water intake wells, etc.) is implemented in models by setting “internal” boundary conditions. Applied problems are analyzed where models of unconfined and confined groundwater flow can be used.