Abstract
The paper deals with the development and research of a mathematical model for hydrophysical processes which involves the use of modern information technologies and computational methods with the aim to improve the accuracy of predictive modeling of ecological condition of shallow waters during the summer. The model takes into account the following factors: movement of water flows; microturbulent diffusion; gravitational settling of pollutants; nonlinear interaction of plankton populations; nutrient, temperature and oxygen regimes; and impact of salinity. A scheme with weights is proposed for the discretization of the proposed model. This scheme significantly reduces both error and computation time. The practical significance of the paper is determined by the software implementation of the model and the determination of the 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 the environment. For this, we consider as an example the Sea of Azov in the summer period. The software parallel implementation involves decomposition methods for computationally intensive diffusion-convection problems taking account of the architecture and parameters of a multiprocessor computer system. The software complex contains a model for fluid dynamics which includes equations of motion in three coordinate directions.
This paper was partially supported by grant No. 17-11-01286 from the Russian Science Foundation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
Park, R.A.: A generalized model for simulating lake ecosystems. J. Simul. 23(2), 33–50 (1974). https://doi.org/10.1177/003754977402300201
Bierman, V.J., Verhoff, 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 Science, Ann Arbor (1974)
Chen, C.W.: Concepts and utilities of ecologic models. J. Sanit. Eng. Div. 96(5), 1085–1097 (1970)
Jorgensen, S.E., Mejer, H., Friis, M.: Examination of a lake model. J. Ecol. Model. 4(2–3), 253–278 (1978). https://doi.org/10.1016/0304-3800(78)90010-8
Williams, B.J.: Hydrobiological Modelling. University of Newcastle, Callaghan (2006)
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, pp. 231–238. Elsevier, Amsterdam-Berlin-London-New York-Tokyo (2005). https://doi.org/10.1016/B978-044452024-1/50030-0
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., 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
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
Sukhinov A., Chistyakov A., Sidoryakina V.: Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids. In: MATEC Web of Conferences XIII International Scientific-Technical Conference “Dynamic of Technical Systems” (DTS-2017), vol. 132, pp. 13–15. Russian Federation, Rostov-on-Don (2017). https://doi.org/10.1051/matecconf/201713204003
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, Selected Papers, Third International Symposium, pp. 37–48. Heidelberg University. AEON Verlag & Studio, Hanau (1995)
Samarsky, A.A., Nikolaev, E.S.: Methods of Solving Grid Equations. Science, Moscow (1978)
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)
SRC “Planeta”. http://planet.iitp.ru/english/index_eng.htm
Samarskiy, A.A.: Theory of Difference Schemes. Nauka, Moscow (1989)
Konovalov, A.N.: The method of steepest descent with adaptive alternately-triangular preamplification. J. Differ. Equat. 40(7), 953 (2004)
Sukhinov, A.I., Chistyakov, A.E., Shishenya, A.V.: Error Estimate of the solution of the diffusion equation on the basis of the schemes with weights. Math. Models Comput. Simul. 6(3), 324–331 (2014). https://doi.org/10.1134/s2070048214030120
Chetverushkin, B., et al.: Unstructured mesh processing in parallel CFD project GIMM. J. Parallel Comput. Fluid Dyn., 501–508 (2005). https://doi.org/10.1016/b978-044452206-1/50061-6
Sukhinov, A.I., Chistyakov, A.E., Semenyakina, A.A., Nikitina, A.V.: Parallel realization of the tasks of the transport of substances and recovery of the bottom surface on the basis of schemes of high order of accuracy. J. Comput. Methods Program.: New Comput. Technol. 16(2), 256–267 (2015)
Chistyakov, A.E., Hachunts, D.S., Nikitina, A.V., Protsenko, E.A., Kuznetsova, I.Y.: Parallel Library of iterative methods of the SLAE solvers for problem of convection-diffusion-based decomposition in one spatial direction. J. Mod. Probl. Sci. Educ. 1(1), 1786 (2015)
Sukhinov, A.I., Nikitina, A.V., Semenyakina, A.A., Protsenko, E.A.: Complex programs and algorithms to calculate sediment transport and multi-component suspensions on a multiprocessor computer system. J. Eng. J. Don 38(4(38)), 52 (2015)
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 the International Scientific Conference Parallel Computational Technologies (PCT 2016), pp. 308–319 (2016)
Nikitina, A.V., Semenyakina, A.A., Chistyakov, A.E.: Parallel implementation of the tasks of diffusion-convection-based schemes of high order of accuracy. J. Vestn. Comput. Inf. Technol. 7(145), 3–8 (2016). https://doi.org/10.14489/vkit.2016.07.pp.003-008
Sukhinov, A.I., Nikitina, A.V., Chistyakov, A.E., Semenov, I.S., Semenyakina, A.A., Khachunts, D.S.: Mathematical modeling of eutrophication processes in shallow waters on multiprocessor computer system. In: CEUR Workshop Proceedings of 10th Annual International Scientific Conference on Parallel Computing Technologies, PCT 2016, 29 March–31 March 2016, Code 121197, vol. 1576, pp. 320–333. Russian Federation, Arkhangelsk (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Sukhinov, A.I., Chistyakov, A.E., Nikitina, A.V., Belova, Y.V., Sumbaev, V.V., Semenyakina, A.A. (2018). Supercomputer Modeling of Hydrochemical Condition of Shallow Waters in Summer Taking into Account the Influence of the Environment. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2018. Communications in Computer and Information Science, vol 910. Springer, Cham. https://doi.org/10.1007/978-3-319-99673-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-99673-8_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99672-1
Online ISBN: 978-3-319-99673-8
eBook Packages: Computer ScienceComputer Science (R0)