An urgent problem related to the process of change in underground water level and mineral salt transfer in soils is solved in the paper. The problem is described by a system of partial differential equations and the corresponding initial, internal and boundary conditions of various kinds. To derive a mathematical model of the process under consideration, a detailed review of scientific papers devoted to various aspects and software of the object of study is given. To conduct a comprehensive study of the process of filtration and change in salt regime of groundwater, mathematical models and an effective numerical algorithm are proposed taking into account external sources and evaporation. Since the process is described by a nonlinear system of partial differential equations, it is difficult to obtain an analytical solution. To solve it, a numerical algorithm based on a finite-difference scheme is developed, and an iterative scheme is used for nonlinear terms, the convergence of the iterative method is checked. In the conclusion of the paper it is shown that the developed mathematical apparatus can significantly reduce the volume of field experiments on monitoring and predicting the level of groundwater and salt concentration and minimize expensive and resource-intensive experimental work.

The paper considers the process of oil-water filtration in a porous medium. To study, predict the main process indicators and make managerial decisions, a mathematical model has been developed, an effective numerical algorithm based on the ideas of differential-difference schemes and the differential sweep method, with the help of which computer experiments can be carried out. When modelling the object of study, the process of displacement of one liquid by another in a porous medium is considered.

Mathematical model for predicting, monitoring and assessing the ecological state of the atmosphere and underlying surface with passive and active impurities is developed in this article; it takes into account the varying rate of particle displacements in the atmosphere. To determine the rate of displacements of fine-dispersed particles in the atmosphere, a system of nonlinear equations has been obtained, which took into account such important factors as: the basic physical-mechanical properties of the particles and the rate of air mass in the atmosphere.

The paper deals with the problem of gas filtration process in a porous medium using a mathematical model of an object; the model is described by a nonlinear partial differential equation and the corresponding boundary and internal conditions. The paper presents the main stages in construction of mathematical model of the process of gas filtration in porous media, taking into account the changes in hydrodynamic parameters of the object of study. To solve the above problem, the following numerical methods have been used: local-one-dimensional schemes and longitudinal-transverse direction schemes. To solve the problem of nonlinear gas filtration in a porous medium, several methods of constructing an iterative process have been checked. To study the responses of the principal parameters of the process, a series of computational experiments on a computer, their analyses and conclusions are given in the paper.

The paper models the spatiotemporal dynamics of the Kattakurgan Reservoir area using satellite-based water and vegetation indices combined with ensemble machinelearning methods. Multi-year time series of NDWI, NDVI, and EVI are used together with meteorological variables (air temperature, humidity, precipitation) from the ERA5 and CHIRPS datasets on the Google Earth Engine platform for 2018–2023. The reservoir water-surface area, derived from satellite imagery, serves as the target variable for training and validating a Random Forest model. The study includes a train–test split, hyperparameter tuning, and performance evaluation using R2, RMSE, and MAE. The results indicate high accuracy: R2 = 0.962 for NDWI prediction, and values close to 1 for reservoir area, with RMSE about 5–7 km2 and MAE 3–5 km2. Forecasts of NDWI and reservoir area for 2024 are produced to assess expected changes in water extent and support water-management decisions and climate adaptation planning.

A mathematical model was developed to numerically study the process of fluid and gas filtration in three-layer interacting pressure porous formations. It is based on the reviews related to the mathematical modeling developed in recent years; it describes a system of partial differential equations with boundary and initial conditions and a conservative numerical algorithm for conducting a computational experiment (CE) on a computer. In this article, to analyze and make managerial decisions, the results of numerical calculations are presented in the form of graphical objects, which can be used to propose schemes for the location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding. Using the proposed mathematical tool, it is possible to obtain the predicted groundwater levels of any area for the required period of time, taking into account some factors, such as the inhomogeneity of the reservoir in a plan, the slope of the confining layer, and other hydrogeological, hydro-technical, and natural conditions, or to calculate the thickness and the optimal location of vertical drainage wells to protect the territory, and to develop oil and gas fields and increase their oil and gas recovery. Analysis of the results of a numerical study of the process made it possible to establish the degrees of influence of the elastic filtration regime in a weakly permeable layer on the overflow into adjacent layers.