Abstract
The work is devoted to mathematical modeling of the scenario for managing the sustainable development of coastal systems using the example of the Azov Sea. The dynamic problem of minimizing the costs of maintaining the ecosystem of the reservoir in a given state, which is interpreted as a requirement for sustainable development, is being solved. The mathematical model of the interaction of two phytoplankton types takes into account the influence of abiotic factors, such as salinity and temperature, on the algae growth, their absorption and excretion of nutrients, as well as the transition of these nutrients from one form to another. For the numerical implementation of the proposed interconnected mathematical models of biological kinetics, parallel algorithms have been developed that are adapted to multiprocessor and hybrid computing systems using the NVIDIA CUDA architecture. An analysis of the characteristics of the CUDA architecture showed the applicability of the algorithms for the numerical implementation of the developed mathematical models of hydrobiology to create high-performance information systems. The constructed software complex allows to simulate the problem of reducing eutrophication and toxicity of the coastal system under consideration by displacing harmful blue-green algae with a cultivated strain of green alga using high performance computing systems.
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References
Williams, B.J.: Hydrobiological Modelling. University of Newcastle, New South Wales (2006)
Nikitina, A., Belova, Y., Atayan, A.: Mathematical modeling of the distribution of nutrients and the dynamics of phytoplankton populations in the Azov Sea, taking into account the influence of salinity and temperature. In: AIP Conference Proceedings, vol. 2188, no. 050027. American Institute of Physics Inc., US (2019). https://doi.org/10.1063/1.5138454
Alekseenko, E., Roux, B., Sukhinov, A., Kotarba, R., Fougere, D.: Nonlinear hydrodynamics in a mediterranean lagoon. J. Comput. Math. Math. Phys. 57(6), 978–994 (2017). https://doi.org/10.5194/npg-20-189-2013
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, pp. 231–238. Elsevier, Amsterdam (2005). https://doi.org/10.1016/B978-044452024-1/50030-0
Riznichenko, G.Y.: Mathematical Models in Biophisics and Ecology. Institute of Computer Research, Moscow-Izhevsk (2003)
Avdeeva, Z.K., Kovriga, S.V., Makarenko, D.I., Maksimov, V.I.: Cognitive approach in the control science. J. Prob. Manage. 3, 2–8 (2007). (in Russian)
Sukhinov, A.I., et al.: Game-theoretic regulations for control mechanisms of sustainable development for shallow water ecosystems. Autom. Remote Control 78(6), 1059–1071 (2017). https://doi.org/10.1134/S0005117917060078
Sukhinov, A.I., Chistyakov, A.E., Nikitina, A.V., Filina, A.A., Belova, Y.V.: Application of high-performance computing for modeling the hydrobiological processes in shallow water. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2019. CCIS, vol. 1129, pp. 166–181. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36592-9_14
Samarskiy, A.A.: Theory of Difference Schemes. Nauka, Moscow (1989)
Konovalov, A.N.: The theory of alternating-triangular iterative method. J. Siberian Math. J. 43(3), 552 (2002)
Sukhinov, A.I., Chistyakov, A.E.: Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator. J. Math. Mod. Comput. Simul. 4(4), 398–409 (2012). https://doi.org/10.1134/S2070048212040084
Chetverushkin, B., et al.: Unstructured mesh processing in parallel CFD project GIMM. In: Parallel Computational Fluid Dynamics, pp. 501–508. Elsevier, Amsterdam (2005)
Sukhinov, A.I., Belova, Y.V., Filina, A.A.: Parallel implementation of substance transport problems for restoration the salinity field based on schemes of high order of accuracy. In: CEUR Workshop Proceedings, vol. 2500. CEUR-WS (2019)
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The reported study was funded by RFBR, project number 20-01-00421.
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Belova, Y., Chistyakov, A., Nikitina, A., Litvinov, V. (2020). Mathematical Modeling of Sustainable Coastal Systems Development Scenarios Based on Game-Theoretic Concepts of Hierarchical Management Using Supercomputer Technologies. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2020. Communications in Computer and Information Science, vol 1331. Springer, Cham. https://doi.org/10.1007/978-3-030-64616-5_22
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