Mathematical Models in Water Use Problems: Development and Practical Applications

Source abstract

Purpose. Currently, water is contaminated in both groundwater sources and surface water sources. This gives rise to a range of challenges related to protecting the aquatic environment from pollution. One of the modern means of protecting groundwater in the presence of aggressive impurities is the use of permeable barriers (reactive barrier). When carrying out design work, it is important to determine the effectiveness of permeable barriers in advance. To solve such a complex problem, it is necessary to have specialized mathematical models. Methodology. The hydrodynamics of groundwater is described by a two-dimensional equation (plan model) of filtration of a pressureless flow of groundwater. To model the process of movement of an aggressive impurity in a groundwater flow, a two-dimensional equation of convective-dispersive propagation of a pollutant in a pressureless flow of groundwater is used. For numerical integration of the equation of filtration of groundwater, two finite-difference splitting schemes are used. For numerical integration of the equation of mass transfer of an aggressive impurity, a splitting scheme by physical processes is used. Findings. The developed numerical models of groundwater dynamics and mass transfer of aggressive impurities were implemented in software. The developed computer codes are a tool for operational analysis of the effectiveness of the use of a permeable barrier. Originality. The solution of the complex problem of geomigration is considered - the movement of an aggressive impurity and its neutralization in a permeable barrier (reactive barrier). To analyze the efficiency of the permeable barrier, a numerical model of groundwater dynamics and mass transfer of an aggressive impurity in groundwater was developed. Based on the developed numerical models, computer codes were developed for conducting computational experiments. Practical value. The constructed numerical models make it possible to quickly solve complex problems in the field of water resource protection from pollution.