Mathematical Modelling as the Basis of the Information System for Monitoring the Aquatic Environment

Abstract

During the project preparation of the construction of the facility, an analysis of the environmental situation at the construction site and adjacent territories, including on water bodies, is carried out. Mathematical modelling of processes in water bodies for monitoring their condition has been performed. Water resources of the region are a complex system of interconnected water bodies that interact with each other and have different characteristics. Analysis of the features of the distribution of pollutants in the aquatic environment of the ecological landscape showed that mathematical modelling should be carried out in three main directions, taking into account the nature of the mass transfer of the substance: diffusion; diffusion-convective; predominantly convective. For each type of mass transfer a mathematical model is created: one-dimensional, two-dimensional or three-dimensional. Under conditions of one-dimensional diffusion, when mass transfer occurs in one predominant direction, two options are considered: 1) diffusion from a point source with a known limited amount of matter; 2) diffusion from a permanently operating source with a known rate of outflow of matter. Both these problems are described by the well-known diffusion equation, but their input and boundary conditions are essentially different. The problem of two-dimensional diffusion was solved for the case when contamination occurs on a certain, rather small part of the boundary of a wide reservoir from a source with constant density. The case of threedimensional spherical diffusion is considered on the example of the solution of the actual problem, when the source of pollution of constant power is at the origin (in the depth of the reservoir). The problem of non-stationary convective diffusion was solved by the example of a flat reservoir with a weak water current, when the simulated region is a wide two-dimensional channel, on the small part of the boundary of which there is a source of a passive impurity. In this case, the known impurity transport equation was used. We used to systematize the potential ecological situation and built the appropriate mathematical models that allowed us to obtain quantitative algorithms for solving the problems of monitoring and developing the components of the information system for calculating the concentrations of pollutants in the water system in the region.