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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 120–137 (Mi zvmmf10768)  

This article is cited in 2 scientific papers (total in 3 papers)

A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation

V. A. Gushchina, A. V. Nikitinab, A. A. Semenyakinac, A. I. Sukhinovd, A. E. Chistyakovd

a Institute for Computer Aided Design, Russian Academy of Sciences, Moscow, Russia
b Research Supercomputer and Neurocomputer Center, Taganrog, Russia
c Don State Technical University, Rostov-on-Don, Russia
d South Federal University, Rostov-on-Don, Russia

Abstract: 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.

Key words: mathematical model, transformation, biogenic materials, phytoplankton, stoichiometric relations, biochemical cycle, coastal system.

Funding Agency Grant Number
Russian Science Foundation 17-11-01286

DOI: https://doi.org/10.31857/S004446690002007-8

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1316–1333

Bibliographic databases:

UDC: 519.635
Received: 05.03.2018

Citation: V. A. Gushchin, A. V. Nikitina, A. A. Semenyakina, A. I. Sukhinov, A. E. Chistyakov, “A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 120–137; Comput. Math. Math. Phys., 58:8 (2018), 1316–1333

Citation in format AMSBIB
\by V.~A.~Gushchin, A.~V.~Nikitina, A.~A.~Semenyakina, A.~I.~Sukhinov, A.~E.~Chistyakov
\paper A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 8
\pages 120--137
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 8
\pages 1316--1333

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Sukhinov, A. E. Chistyakov, A. A. Filina, A. V. Nikitina, V. N. Litvinov, “Supercomputer simulation of oil spills in the Azov Sea”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:3 (2019), 115–129  mathnet  crossref  elib
    2. S. V. Protsenko, A. M. Atayan, A. E. Chistyakov, A. V. Nikitina, V. N. Litvinov, A. A. Filina, “Eksperimentalnoe issledovanie silovykh nagruzok na opory nadvodnoi konstruktsii na osnove matematicheskoi modeli volnovykh protsessov”, Vestn. YuUrGU. Ser. Vych. matem. inform., 8:3 (2019), 27–42  mathnet  crossref  elib
    3. “Abstracts of talks given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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