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This paper describes a three-dimensional mathematical hydrodynamic model capable of taking into account the processes of salt and heat transfer in the Azov Sea. The model allows obtaining three-dimensional fields of the vector of water flow rates, pressure, sea water density, salinity and temperature. The model is based on the equations of motion (Navier-Stokes), the continuity equation in the case of variable density, and the equations of heat and salt transport. The boundary and initial conditions are indicated. To approximate the equation of diffusion-convection-reaction in time, we analyzed the schemes with weights. The approximation of the problem of calculating the velocity field of the aquatic environment in terms of spatial variables was carried out on the basis of the balance method taking into account the occupancy ratios of the control areas. The stationary modes of the heat and salt transfer problem were investigated. The initial distribution of the salinity and temperature functions, which have a sufficient degree of smoothness at the points of setting the field values, was calculated using the Laplace equation. Using the interpolation algorithm and by superimposing the boundaries of the region, maps of salinity and temperature of the Sea of Azov were obtained. Based on the monitoring of the water area, three-dimensional mathematical models of the movement of the aquatic environment designed to predict possible scenarios for the development of the Azov Sea ecosystem were constructed in order to avoid the occurrence of anaerobic infection areas and take timely measures for their localization. The full-scale data obtained using different types of measuring instruments was used to develop observation models for prediction of the changes in hydrodynamic processes. A modified Kalman filter algorithm was applied to obtain unbiased minimum-variance state estimation for the dynamic system. A description is given of a software package that allows modeling hydrodynamic processes in shallow water bodies with complex spatial structures of currents, taking into account the transport of salts and heat. |
