The work contains the construction and software implementation of related software systems designed for mathematical modeling of processes occurring in coastal water systems. The space-two-dimensional model of sediment transport in shallow waters allows to forecast the dynamics of bottom topography changes by reason of the movement of water and solid particles, to take into account the porosity of the soil, the critical shear stress at which begins the movement of sediment, turbulent exchange, dynamically changing geometry of the bottom, wind currents and friction on the bottom. The mathematical model of motion of a multicomponent air, takes into account factors such as the transport of pollutants and heat; the effect of vegetation; change in the coefficient of turbulent exchange; water transfer from the liquid to the gaseous state and others.

Keywords: multiprocessor computer system, grid equations, suspended solids, sediment

In this article the mathematical model of transformation of biogenous substances forms, such as phosphorus, nitrogen and silicon, in water ecosystems by the example of the Azov Sea is constructed. The model considers absorption and excretion of nutrients by phytoplankton, and also transition of substances from one form to another. The equations system that describing model was studied for what linearization of system was made, the square functional was constructed. As a result of research sufficient conditions of uniqueness of the problem solution were received, the theorem was formulated.

Keywords: phytoplankton, phosphorus, nitrogen, silicon, biogene, chemical and biological source, equation of convection-diffusion-reaction, linearization, uniqueness of the decision of equations system