Mathematical modeling of biogeochemical cycles in coastal systems of the South of Russia

This work is devoted to the development and study of a mathematical model of biogeochemical processes occurring in the coastal systems of southern Russia, which makes it possible to improve the accuracy of predicting the dynamics of phytoplankton populations, taking into account the effect of salinity and temperature on their development and transformation of forms of phosphorus, nitrogen and silicon. The study of the continuous model is carried out, the linearization of nonlinear functions of sources is carried out, and sufficient conditions for the uniqueness of solutions of chains of initial-boundary value problems interrelated in initial and final conditions are obtained, and a theorem is formulated. Difference schemes are constructed based on improved discretization of advective terms of linearized initial-boundary value problems on a spatial grid, based on linear combinations of cabaret and central-difference schemes. These schemes have better accuracy and increased stability margin (applicable in a wider range of grid Peclet numbers) compared to traditional difference schemes. Initial conditions and refined parameters of the system of equations are obtained, salinity and temperature fields for the Azov Sea, which have a sufficient degree of smoothness, are reconstructed from hydrographic maps. A software package was developed and a numerical experiment was carried out on diagnostic and predictive modeling of biogeochemical processes in the Azov Sea in the summer under conditions of modern salinity. The simulation results are consistent with the available observational data.