The program designed to simulate possible scenarios of the ecosystem and a numerical experiment was builds. The problem of transport materials was solved. Drain and obstacles inversion transport substances fairly accurately restores the initial location of the site of contamination was shown upon slight movement of contaminants regardless of the location in a predetermined region of the source.

Keywords: Inverse problem, numerical solution, the concentration of substances, distribution, water environment, pollution

The work is devoted to modeling sediment transport in shallow waters. Results of mathematical and numerical modeling can be applied in practice to justify the design and construction of hydraulic structures to predict the formation of the bottom topography (eg predicting sediment transport), to address issues related to the protection of the recorded ports and channels, weather impacts to the design, to determine the optimal routes maritime access channels, etc.

Keywords: mathematical modeling, hydrodynamics, transport of substances, the Navier-Stokes equation of diffusion-convection-reaction

A modified analog-SSOR of variation type is used for numerical realization of two-dimensional discrete mathematical model of the aquatic environment, which is based on a three-dimensional hydrostatic model. Governing equations of the given model are equations for incompressible fluid, hydrostatic equation and Navier-Stokes equation. Developed model is used to predict the processes of sedimentation and the impact of negative factors affecting the condition of coastal and offshore structures. An algorithm for the minimal residuals modified analog-SSOR method for solving the difference equations is presented in the paper. The results of numerical experiments are presented.

Keywords: Iterative methods, hydrodynamics, discrete model, grid education, Navier-Stokes equation.