Data processing of field measurements of expedition research for mathematical modeling of hydrodynamic processes in the Azov Sea
DOI:
https://doi.org/10.7242/1999-6691/2020.13.2.13Keywords:
mathematical modeling, hydrodynamics, turbulent exchange, shallow water, Kalman filter, expedition researchAbstract
This paper describes a three-dimensional mathematical hydrodynamic model capable of taking into account the processes of salt and heat transfer in the Azov Sea. The model allows obtaining three-dimensional fields of the vector of water flow rates, pressure, sea water density, salinity and temperature. The model is based on the equations of motion (Navier-Stokes), the continuity equation in the case of variable density, and the equations of heat and salt transport. The boundary and initial conditions are indicated. To approximate the equation of diffusion-convection-reaction in time, we analyzed the schemes with weights. The approximation of the problem of calculating the velocity field of the aquatic environment in terms of spatial variables was carried out on the basis of the balance method taking into account the occupancy ratios of the control areas. The stationary modes of the heat and salt transfer problem were investigated. The initial distribution of the salinity and temperature functions, which have a sufficient degree of smoothness at the points of setting the field values, was calculated using the Laplace equation. Using the interpolation algorithm and by superimposing the boundaries of the region, maps of salinity and temperature of the Sea of Azov were obtained. Based on the monitoring of the water area, three-dimensional mathematical models of the movement of the aquatic environment designed to predict possible scenarios for the development of the Azov Sea ecosystem were constructed in order to avoid the occurrence of anaerobic infection areas and take timely measures for their localization. The full-scale data obtained using different types of measuring instruments was used to develop observation models for prediction of the changes in hydrodynamic processes. A modified Kalman filter algorithm was applied to obtain unbiased minimum-variance state estimation for the dynamic system. A description is given of a software package that allows modeling hydrodynamic processes in shallow water bodies with complex spatial structures of currents, taking into account the transport of salts and heat.
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References
Marchuk G.I., Kagan B.A. Dinamika okeanskikh prilivov [Ocean tide dynamics]. Leningrad, Gidrometeoizdat, 1983. 359 p.
Matishov G.G., Il’ichev V.G. Optimal utilization of water resources: The concept of internal prices. Dokl. Earth Sc., 2006, vol. 406, pp. 86-88. https://doi.org/10.1134/S1028334X06010211">https://doi.org/10.1134/S1028334X06010211
Yakushev E.V., Mikhailovsky G.E. Mathematical modeling of the influence of marine biota on the carbon dioxide ocean-atmosphere exchange in high latitudes. Air-Water Gas Transfer. Selected papers from the Third Int. Symp., ed. B. Jaehne, E.C. Monahan. Hanau: AEON Verlag Studio, 1995. P. 37-48.
Lyubimova T.P., Lepikhin A.P., Parshakova Ya.N., Gualt'eri C., Lane S.N., Roux B. Influence of hydrodynamic regimes on mixing of waters of confluent rivers. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2018, vol. 11, no. 3, pp. 354-361. https://doi.org/10.7242/1999-6691/2018.11.3.26">https://doi.org/10.7242/1999-6691/2018.11.3.26
Lyubimova T.P., Lepikhin A.P., Parshakova Ya.N. Numerical simulation of wastewater discharge into water objects to improve discharge devices. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2019, vol. 12, no. 4, pp. 427-434. https://doi.org/10.7242/1999-6691/2019.12.4.36">https://doi.org/10.7242/1999-6691/2019.12.4.36
Lyubimova T.P., Parshakova Ya.N. Modeling propagation of thermal pollution in large water bodies. Voda i ekologiya: problemy i resheniya – Water and ecology, 2019, no. 2(78), pp. 92-101. https://doi.org/10.23968/2305-3488.2019.24.2.92-101">https://doi.org/10.23968/2305-3488.2019.24.2.92‑101
Parshakova Ya.N., Lyubimova T.P., Lyakhin Yu.S., Lepikhin A.P. Computer simulation of thermal processes in water bodies under different hydrometeorological conditions. J. Phys.: Conf. Ser., 2019, vol. 1163, 012034. https://doi.org/10.1088/1742-6596/1163/1/012034">https://doi.org/10.1088/1742-6596/1163/1/012034
Oliger J., Sundstorm A. Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. SIAM J. Appl. Math., 1978, vol. 35, pp. 419-446.
Marchesiello P., McWilliams J.C., Shchepetkin A. Open boundary conditions for long-term integration of regional oceanic models. Ocean Model., 2001, vol. 3, pp. 1-20. https://doi.org/10.1016/S1463-5003(00)00013-5">https://doi.org/10.1016/S1463-5003(00)00013-5
Vol’tsinger N.E., Klevannyy K.A., Pelinovskiy E.N. Dlinnovolnovaya dinamika pribrezhnoy zony [The long-wave dynamics of the coastal zone]. Leningrad, Gidrometeoizdat, 1989. 271 p.
Androsov A.A., Vol’tsinger N.E. Prolivy mirovogo okeana. Obshchiy podkhod k modelirovaniyu [Straits of the oceans. General approach to modeling]. St. Petersburg, Nauka, 2005. 188 p.
Tran J.K. A predator-prey functional response incorporating indirect interference and depletion. Verh. Internat. Verein Limnol., 2008, vol. 30, pp. 302-305.
Alekseenko E., Roux B., Sukhinov A., Kotarba R., Fougere D. Coastal hydrodynamics in a windy lagoon. Comput. Fluid., 2013, vol. 77, pp. 24-35. https://doi.org/10.1016/j.compfluid.2013.02.003">https://doi.org/10.1016/j.compfluid.2013.02.003
Sukhinov A.I, Chistyakov A.E., Alekseenko E.V. Numerical realization of three-dimensional model of hydrodynamics for shallow water basins on high-performance system. Math. Models Comput. Simul., 2011, vol. 3, pp. 562-574. https://doi.org/10.1134/S2070048211050115">https://doi.org/10.1134/S2070048211050115
Sukhinov A.I., Chistyakov A.E., Shishenya A.V., Timofeeva E.F. Predictive modeling of coastal hydrophysical processes in multiple-processor systems based on explicit schemes. Math. Models Comput. Simul., 2018, vol. 10, pp. 648-658. https://doi.org/10.1134/S2070048218050125">https://doi.org/10.1134/S2070048218050125
Sukhinov A.I., Nikitina A.V., Chistyakov A.E., Semenov I.S. Mathematical modeling of the formation of suffocation conditions in shallow basins using multiprocessor computing systems. Vych. met. programmirovaniye – Numerical Methods and Programming, 2013, vol. 14, no. 1, pp. 103-112.
Sukhinov A., Isayev A., Nikitina A., Chistyakov A., Sumbaev V., Semenyakina A. Complex of models, high-resolution schemes and programs for the predictive modeling of suffocation in shallow waters. Parallel Computational Technologies. PCT 2017, ed. L. Sokolinsky, M. Zymbler. Springer, 2017. P. 169-185. https://doi.org/10.1007/978-3-319-67035-5_13">https://doi.org/10.1007/978-3-319-67035-5_13
Sukhinov A.I., Protsenko E.A., Chistyakov A E., Shreter S.A. Comparison of computational efficiency of explicit and implicit schemes for the sediment transport problem in coastal zones. Vych. met. programmirovaniye – Numerical Methods and Programming, 2015, vol. 16, no. 3, pp. 328-338. https://doi.org/10.26089/NumMet.v16r332">https://doi.org/10.26089/NumMet.v16r332
Gushchin V.A., Sukhinov A.I., Nikitina A.V., Chistyakov A.E., Semenyakina A.A. A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation. Comput. Math. and Math. Phys., 2018, vol. 58, pp. 1316-1333. https://doi.org/10.1134/S0965542518080092">https://doi.org/10.1134/S0965542518080092
Belotserkovskiy O.M., Oparin A.M., Chechetkin V.M. Turbulentnost’. Novyye podkhody [Turbulence. New approaches]. Moscow, Nauka, 2003. 286 p.
Fofonoff N.P., Millard Jr. R.C. Algorithms for the computation of fundamental properties of seawater. Unesco, 1983. 53 p. http://hdl.handle.net/11329/109">http://hdl.handle.net/11329/109
Samarskiy A.A., Vabishchevich P.N. Chislennyye metody resheniya zadach konvektsii-diffuzii [Numerical methods for solving convection-diffusion problems]. Мoscow, URSS, 2009. 246 p.
Konovalov A.N. The steepest descent method with an adaptive alternating-triangular preconditioner. Differential Equations, 2004, vol. 40, pp. 1018-1028. https://doi.org/10.1023/B:DIEQ.0000047032.23099.e3">https://doi.org/10.1023/B:DIEQ.0000047032.23099.e3
Kalman R.E. A new approach to linear filtering and prediction problems. J. Basic Eng., 1960, vol. 82, pp. 35-45. https://doi.org/10.1115/1.3662552">https://doi.org/10.1115/1.3662552
Kalman Filter – Introduction [Electronic resource] URL: https://baumanka.pashinin.com/IU2/sem11/Фильтр%20Калмана/Проги/калman/Фильтр%20Калмана%20—%20Введение%20%20%20Хабрахабр.html">https://baumanka.pashinin.com/IU2/sem11/Filtr%20 Calmana /Progi/calman/ Filtr %20 Calmana %20—%20Vvedenie%20%20%20Khabrakhabr.html (accessed 25 June 2020).
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