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The paper covers the modeling of hydrodynamic processes in shallow waters in the presence of pollutants of various types, as well as areas covered with plastic waste, including nano- and microplastics. The simulation performed using new and effective mathematical instruments, including assimilation methods of measurement data, restoration of the state function, diagnostics of quality of the developed models, the research the sensitivity of models to variations in input data, the integration of models with various scales. Interrelated non-stationary, spatially inhomogeneous mathematical models of hydrodynamics and biological kinetics of shallow waters were developed and numerically implemented. They describe non-linear processes of hydrophysics, biogeochemical cycles, transport and transformation of suspensions and sediments with microplastic particles and other pollutants, absorption of it by zooplankton and fish, movement of plastic particles through food, the forecast of their impact on the main hydrobionts of shallow waters of the Azov-Black Sea basin, including the Azov Sea, Taganrog Bay, Gelendzhik Bay. The models take into account the heat and salt transport; the complex, dynamically changing water geometry; friction on the bottom and wind stresses; turbulent and advective heat and mass exchange in three coordinate directions; the Coriolis force; river flows; evaporation, temperature and oxygen regimes. They make it possible to improve the accuracy of hydrophysical processes modeling in shallow waters, to detect vortex structures of currents that can be a natural pollution traps, including microplastic. Based on a supercomputer, a complex of application has been designed and adapted for solving predictive problems of water ecology and water resources management.

Software has been developed in the C++ programming language using the MPI parallel programming technology, designed for mathematical modeling of the transport of substances in coastal systems. When calculating the dynamics of the spread of a pollutant, the decomposition of the computational domain was carried out to organize the computational process on a multiprocessor computer system K-60 in KIAM RAS. To solve the system of grid equations obtained as a result of the approximation of the problem, iterative methods were used, with a triangular preconditioner.

The paper presents currently used approaches to the assessment of water pollution by various types of pollutants. Based on the existing criteria, an algorithm for assessing risks and vulnerability to anthropogenic impacts is proposed. The software package obtained on their basis makes it possible to model the processes of the spread of pollutants in the studied water area, to detect and evaluate the power of sources of pollutants and manage them, to assess risks and vulnerabilities in relation to anthropogenic impacts, to carry out zoning of the water area of a shallow water body in accordance with the levels of anthropogenic loads, to carry out environmental design from the standpoint of sustainable development.

A method for solving grid equations in areas with geometry "stretched" along one of the spatial directions is proposed. Method proposed for model includes pollutants whose concentration in the Azov Sea, according to the analysis of scientific publications and environmental databases, exceeds the maximum permissible concentration (MPC). The mechanism of the preconditioner formation is described. The estimation of the minimum and maximum eigenvalues is performed. Using object-oriented analysis and design, a class library has been implemented to solve the problem of impurity propagation in a shallow reservoir. The architecture of an information system to support scientific research capable of functioning in conditions of using heterogeneous computing environments is described. The system is based on the requirement of the maximum possible use of free software in order to minimize capital and operational costs. The system uses classes that allow you to read and write information about the geometry of the object under study and the parameters of the calculated grid. Numerical experiments were carried out using the developed software package, including the proposed mathematical model, focused on the multiprocessor computing system (MCS). The dependences of the SLAE solution time on the number of diagonals and the order of the matrix are obtained. The number of iterations for solving grid equations has been experimentally determined depending on the ratio of the number of nodes in spatial coordinates.