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Application of High-Performance Computing for Modeling the Hydrobiological Processes in Shallow Water

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Supercomputing (RuSCDays 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1129))

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Abstract

The paper covers the development and research of a mathematical model for description hydrobiological processes using the modern information technologies and computational methods to improve the accuracy of predictive modeling the ecological situation in shallow waters. The model takes into account the following factors: movement of water flows; microturbulent diffusion; gravitational settling of pollutants; nonlinear interaction of phyto- and zooplankton populations; nutrient, temperature and oxygen regimes; and influence of salinity. A space splitting scheme taking into account the partial filling of cells was proposed for model discretization. This scheme significantly reduces both error and calculation time. The practical significance of the paper is determined by software implementation of the model and the determination of limits and prospects of its practical use. Experimental software is designed on the basis of a supercomputer for mathematical modeling of possible development scenarios of shallow water ecosystems taking into account the influence of environment. For this, we consider as an example the Azov Sea in summer. The parallel implementation involves decomposition methods for computationally laborious diffusion-convection problems taking into account the architecture and parameters of a multiprocessor computer system.

This paper was partially supported by grant No. 17-11-01286 of the Russian Science Foundation.

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References

  1. Lotka, A.J.: Contribution to the energetics of evolution. Proc. Natl. Acad. Sci. 8, 147–150 (1922)

    Article  Google Scholar 

  2. Volterra, V.: Variations and fluctuations of the number of individuals in animal species living together. Rapp. P. - V. Reun. Cons. Int. Explor. Mer. 3, 3–51 (1928)

    Article  Google Scholar 

  3. Logofet, D.O., Lesnaya, E.V.: The mathematics of Markov models: what Markov chains can really predict in forest successions. J. Ecol. Modell. 126, 285–298 (2000)

    Article  Google Scholar 

  4. Monod, J.: Recherches sur la croissance des cultures bacteriennes. Hermann, Paris (1942). 210 p

    Google Scholar 

  5. Mitscherlich, E.A.: Das Gesertz des Minimums und das Gesetz des Abnehmenden Bodenertrags. J. Landw. Jahrb 38, 595 (1909)

    Google Scholar 

  6. Vinberg, G.G.: Some results of the practice of production- hydrobiological methods. In: Production of populations and communities of aquatic organisms and methods of its research. Sverdlovsk: UNC AN USSR, pp. 3–18 (1985)

    Google Scholar 

  7. Abakumov, A.I.: Signs of of water ecosystems stability in mathematical models. In: Proceedings of the Institute of System Analysis of RAS. System Analysis of the Problem of Sustainable Development. M: ISA RAS, vol. 54, pp. 49–60 (2010)

    Google Scholar 

  8. Menshutkin, V.V.: The skill of modeling (ecology, physiology, evolution). Petrozavodsk; St. Petersburg (2010). 419 p

    Google Scholar 

  9. Menshutkin, V.V., Rukhovets, L.A., Filatov, N.N.: Modeling of freshwater lake ecosystems (review). 2. Models of freshwater lake ecosystems. J. Water Resour. 41(1), 24–38 (2014)

    Google Scholar 

  10. Vorovich, I.I., et al.: Rational use of water resources of the Azov Sea basin: mathematical models. Science (1981). 360 p

    Google Scholar 

  11. Jørgensen, S.E., Fu-Liu, X., Jorgensen, S.E., Tao, S., Li, B.-G.: J. Ecol. Model. 117, 239–260 (1999)

    Article  Google Scholar 

  12. Vollenweider, R.A.: Scientific fundamentals of the Eutrophication of lakes and flowing waters, with particular reference to nitrogen and phosphorus as factors in Eutrophication OECD. Paris. Tech Report DA 515C1168 27 (1968). 250 p

    Google Scholar 

  13. Matishov, G.G., Ilyichev, V.G.: On optimal exploitation of water resources. The concept of domestic prices. Rep. Acad. Sci. 406(2), 249–251 (2006)

    Google Scholar 

  14. Tyutyunov, Y.V., Titova, L.I.: Simple models for studying complex spatiotemporal patterns of animal behavior. J. Deep-Sea Res. II(140), 193–202 (2017)

    Google Scholar 

  15. Perevaryukha, A.Y.: Hybrid model of bioresourses’ dynamics: equilibrium, cycle, and transitional chaos. J. Autom. Control Comput. Sci. 45(4), 223–232 (2011)

    Article  Google Scholar 

  16. Samarskiy, A.A.: Theory of difference schemes. Science (1989). 616 p

    Google Scholar 

  17. Marchuk, G.I., Shutyaev, V.P.: Adjoint equations and iterative algorithms in problems of variational data assimilation. Proc. Steklov Inst. Math. (Suppl.) 276(suppl. 1), 138–152 (2012)

    Article  MathSciNet  Google Scholar 

  18. Marchuk, G.I., Sarkisyan, A.S.: Mathematical modelling of ocean circulation. Science (1988). 297 p

    Google Scholar 

  19. Chetverushkin, B., et al.: Unstructured mesh processing in parallel CFD project GIMM. In: Parallel Computational Fluid Dynamics, Amsterdam, Elsevier, pp. 501–508 (2005). https://doi.org/10.1016/b978-044452206-1/50061-6

    Chapter  Google Scholar 

  20. Yakushev, E.V., Mikhailovsky, G.E.: Mathematical modeling of the influence of marine biota on the carbon dioxide ocean-atmosphere exchange in high latitudes. In: Jaehne, B., Monahan, E.C. (eds.) Air-Water Gas Transfer, Sel. Papers, Third Int. Symp., Heidelberg University, AEON Verlag & Studio, Hanau, pp. 37–48 (1995)

    Google Scholar 

  21. Van Straten, G., Keesman, K.J.: Uncertainty propagation and speculation in projective forecasts of environmental change: a lake eutrophication example. J. Forecast. 10, 163–190 (1991). https://doi.org/10.1002/for.3980100110

    Article  Google Scholar 

  22. Sukhinov, A.I., Sukhinov, A.A.: Reconstruction of 2001 ecological disaster in the azov sea on the basis of precise hydrophysics models. In: Parallel Computational Fluid Dynamics, Multidisciplinary Applications, Proceedings of Parallel CFD 2004 Conference, Las Palmas de Gran Canaria, Spain, ELSEVIER, Amsterdam-Berlin-London-New York-Tokyo, pp. 231–238 (2005). https://doi.org/10.1016/B978-044452024-1/50030-0

    Chapter  Google Scholar 

  23. Park, R.A.: A generalized model for simulating lake ecosystems. J. Simul. 23(2), 33–50 (1974). https://doi.org/10.1177/003754977402300201

    Article  Google Scholar 

  24. Bierman, V.J., Verho, F.H., Poulson, T.C., Tenney, M.W.: Multinutrient dynamic models of algal growth and species competition in eutrophic lakes. In: Modeling the Eutrophication Process. Ann Arbor: Ann Arbor Science (1974)

    Google Scholar 

  25. Monin, A.S.: Turbulence and microstructure in Ocean. J. Adv. Phys. Sci. 109(2), 333–353 (1973)

    Google Scholar 

  26. Alekseenko, E., Roux, B., Sukhinov, A., Kotarba, R., Fougere, D.: Nonlinear hydrodynamics in a mediterranean lagoon. J. Nonlin. Process. Geophys. 20(2), 189–198 (2013). https://doi.org/10.5194/npg-20-189-2013

    Article  Google Scholar 

  27. Sidoryakina, V.V., Sukhinov, A.I.: Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problem. J. Comput. Math. Math. Phys. 57(6), 978–994 (2017). https://doi.org/10.1134/s0965542517060124

    Article  MathSciNet  MATH  Google Scholar 

  28. Sukhinov, A.I., Chistyakov, A.E., Alekseenko, E.V.: Numerical realization of the three-dimensional model of hydrodynamics for shallow water basins on a high-performance system. J. Math. Models Comput. Simul. 3(5), 562–574 (2011). https://doi.org/10.1134/s2070048211050115

    Article  MathSciNet  MATH  Google Scholar 

  29. Samarsky, A.A., Nikolaev, E.S.: Methods of solving grid equations. Science (1978). 532 p

    Google Scholar 

  30. Konovalov, A.N.: The method of steepest descent with adaptive alternately-triangular preamplification. J. Diff. Equat. 40(7), 953 (2004)

    Google Scholar 

  31. Sukhinov, A.I., Chistyakov, A.E.: Adaptive modified alternating triangular iterative method for solving grid equations with non-selfadjoint operator. J. Math. Models Comput. Simul. 24(1), 3–20 (2012)

    MATH  Google Scholar 

  32. Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E.: A set of models, explicit regularized schemes of high order of accuracy and programs for predictive modeling of consequences of emergency oil spill. In: Proceedings of 10th Annual International Scientific Conference on Parallel computational technologies (PCT 2016), Arkhangelsk. Chelyabinsk: Publishing center SUSU, pp. 308–319 (2016)

    Google Scholar 

  33. SRC “Planeta”. http://planet.iitp.ru/english/index_eng.htm

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Correspondence to Alla V. Nikitina .

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Sukhinov, A.I., Chistyakov, A.E., Nikitina, A.V., Filina, A.A., Belova, Y.V. (2019). Application of High-Performance Computing for Modeling the Hydrobiological Processes in Shallow Water. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2019. Communications in Computer and Information Science, vol 1129. Springer, Cham. https://doi.org/10.1007/978-3-030-36592-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-36592-9_14

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