Gushchin, V. A.; Sukhinov, A. I.; Nikitina, A. V.; Chistyakov, A. E.; Semenyakina, A. A. A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation. (English. Russian original) Zbl 1404.86002 Comput. Math. Math. Phys. 58, No. 8, 1316-1333 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 8 (2018). Summary: A discrete mathematical model of hydrobiology of coastal zone is constructed and analyzed. The model takes into account the transport and transformation of polluting biogenic elements in water basins. The propagation and transformation of biogenic elements is affected by such physical factors as three-dimensional motion of water taking into account the advective transport and microturbulent diffusion, spatially inhomogeneous distribution of temperature, salinity, and oxygen. Biogenic pollutants typically arrive into the water basin with river flow, which depends on the weather and climate of the geographic region, or with drainage of insufficiently purified domestic and industrial waste or other kinds of anthropogenic impact. Biogenic pollutants can also appear due to secondary pollution processes, such as stirring up and transport of bed silt, shore abrasion, etc. Stoichiometric relations between biogenic nutrients for phytoplankton algae that can be used to determine the limiting nutrient for each species are obtained. Observation models describing the consumption, accumulation of nutrients, and growth of phytoplankton are considered. A three-dimensional mathematical model of transformation of forms of phosphorus, nitrogen, and silicon in the plankton dynamics problem in coastal systems is constructed and analyzed. This model takes into account the convective and diffusive transport, absorption, and release of nutrients by phytoplankton as well as transformation cycles of phosphorus, nitrogen, and silicon forms. Numerical methods for solving the problem that are based on high-order weighted finite difference schemes and take into account the degree of fill of the computation domain control cells are developed. These methods are implemented on a multiprocessing system. They make it possible to improve the accuracy of the numerical solution and decrease the computation time by several fold. Based on the numerical implementation, dangerous phenomena in coastal systems related to the propagation of pollutants, including oil spill, eutrophication, and algae bloom, which causes suffocation phenomena in water basins, are reconstructed. MSC: 86-08 Computational methods for problems pertaining to geophysics 92D40 Ecology 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 86A05 Hydrology, hydrography, oceanography Keywords:mathematical model; transformation; biogenic materials; phytoplankton; stoichiometric relations; biochemical cycle; coastal system PDF BibTeX XML Full Text: DOI References:  G. I. Marchuk, Mathematical Modeling of the Environment (Nauka, Moscow, 1982) [in Russian]. · Zbl 0493.90001  Davydov, A. A.; Chetverushkin, B. N.; Shil’nikov, E. V., Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems, Comput. Math, Math. Phys., 50, 2157-2165, (2010) · Zbl 1224.65326  Chetverushkin, B. N., Resolution limits of continuous media mode and their mathematical formulations, Math. Models Comput. Simul., 5, 266-279, (2013)  A. I. Sukhinov and A. A. 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