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 Computer Research and Modeling, 2016, Volume 8, Issue 1, Pages 151–168 (Mi crm136)

ANALYSIS AND MODELING OF COMPLEX LIVING SYSTEMS

Numerical modeling of ecologic situation of the azov sea with using schemes of increased order of accuracy on multiprocessor computer system

A. I. Sukhinova, A. E. Chistyakovb, A. A. Semenyakinab, A. V. Nikitinab

a Don state technical University, 1 Gagarin sq., Rostov-on-don, 344000, Russia
b Scientific Researches Institute of Multiprocessor Comput er Systems of academician A. V. Kalyaev of South Federal University, 2 Chekhov st., Taganrog, Rostov region, 347922, Russia

Abstract: The article covered results of three-dimensional modeling of ecologic situation of shallow water on the example of the Azov Sea with using schemes of increased order of accuracy on multiprocessor computer system of Southern Federal University. Discrete analogs of convective and diffusive transfer operators of the fourth order of accuracy in the case of partial occupancy of cells were constructed and studied. The developed scheme of the high (fourth) order of accuracy were used for solving problems of aquatic ecology and modeling spatial distribution of polluting nutrients, which caused growth of phytoplankton, many species of which are toxic and harmful. The use of schemes of the high order of accuracy are improved the quality of input data and decreased the error in solutions of model tasks of aquatic ecology. Numerical experiments were conducted for the problem of transportation of substances on the basis of the schemes of the second and fourth orders of accuracy. They’re showed that the accuracy was increased in 48.7 times for diffusion-convection problem. The mathematical algorithm was proposed and numerically implemented, which designed to restore the bottom topography of shallow water on the basis of hydrographic data (water depth at individual points or contour level). The map of bottom relief of the Azov Sea was generated with using this algorithm. It’s used to build fields of currents calculated on the basis of hydrodynamic model. The fields of water flow currents were used as input data of the aquatic ecology models. The library of double-layered iterative methods was developed for solving of nine-diagonal difference equations. It occurs in discretization of model tasks of challenges of pollutants concentration, plankton and fish on multiprocessor computer system. It improved the precision of the calculated data and gave the possibility to obtain operational forecasts of changes in ecologic situation of shallow water in short time intervals.

Keywords: mathematical model, scheme of high order of accuracy, bottom topography, transport of substances, aquatic ecology tasks, Azov Sea, multiprocessor computer system.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 2014/174

DOI: https://doi.org/10.20537/2076-7633-2016-8-1-151-168

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UDC: 519.8
Revised: 25.11.2015

Citation: A. I. Sukhinov, A. E. Chistyakov, A. A. Semenyakina, A. V. Nikitina, “Numerical modeling of ecologic situation of the azov sea with using schemes of increased order of accuracy on multiprocessor computer system”, Computer Research and Modeling, 8:1 (2016), 151–168

Citation in format AMSBIB
\Bibitem{SukChiSem16} \by A.~I.~Sukhinov, A.~E.~Chistyakov, A.~A.~Semenyakina, A.~V.~Nikitina \paper Numerical modeling of ecologic situation of the azov sea with using schemes of increased order of accuracy on multiprocessor computer system \jour Computer Research and Modeling \yr 2016 \vol 8 \issue 1 \pages 151--168 \mathnet{http://mi.mathnet.ru/crm136} \crossref{https://doi.org/10.20537/2076-7633-2016-8-1-151-168} 

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This publication is cited in the following articles:
1. A. I. Sukhinov, A. V. Nikitina, A. E. Chistyakov, A. A. Semenyakina, “Practical aspects of implementation of the parallel algorithm for solving problem of ctenophore population interaction in the Azov Sea”, Vestn. YuUrGU. Ser. Vych. matem. inform., 7:3 (2018), 31–54
2. 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”, Comput. Math. Math. Phys., 58:8 (2018), 1316–1333
3. “Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169
4. 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
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