Application of the regularized shallow water equations for numerical simulation of casavie fluctuations in the Azov sea
Matematičeskoe modelirovanie, Tome 29 (2017) no. 1, pp. 45-62.

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Mathematical model and related finite-volume scheme for sea level evolution in the framework of regularized shallow water equations are described. Numerical algorithm is adapted to the topology and natural features of the Azov sea. Results of calculations of hydrodynamic flows in a typical sasevich (casavie) fluctuations in the Azov sea, emerging under the influence tidal or wind influences, are presented.
Keywords: regularized shallow water equations, finite-volume scheme, Azov sea.
Mots-clés : casavie fluctuations
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T. G. Elizarova; D. S. Saburin. Application of the regularized shallow water equations for numerical simulation of casavie fluctuations in the Azov sea. Matematičeskoe modelirovanie, Tome 29 (2017) no. 1, pp. 45-62. http://geodesic.mathdoc.fr/item/MM_2017_29_1_a3/

[1] S. F. Dotsenko, V. A. Ivanov, Prirodnye katastrofy Azovsko-Chernomorskogo regiona, NAN Ukrainy, Morskoi gidrofizitseslii institut, Sevastopol, 2010

[2] V. B. Zalesny, A. V. Gusev, S. N. Moshonkin, “Numerical model of the hydrodynamics of the Black Sea and the Sea of Azov with variational initialization of temperature and salinity”, Izv. Atmos. Ocean. Phys., 49:6 (2013), 642–658 | DOI | DOI

[3] V. V. Zalesny, N. A. Diansky, V. V. Fomin et al., “Numerical model of the circulation of the Black Sea and the Sea of Azov”, Russian Journal of Numerical Analysis and Mathematical Modelling, 27:1 (2012), 95–111 | DOI

[4] V. V. Fomin, A. A. Polozok, R. V. Kamyshnikov, “Wave and storm surge modelling for Sea of Azov with use of swan+adcirc”, Geoinformation Sciences and Environmental Development: New Approaches, Methods, Technologies, Collection of articles of the II Internati (Limassol, Cyprus, 2014), Rostov-on-Don, 2014, 111–116

[5] G. G. Matishov, Yu. I. Inzhebeikin, “Numerical study of the Azov Sea level seiche oscillations”, Oceanology, 49:4 (2009), 445–452 | DOI

[6] Yu. G. Filippov, “Natural fluctuations of the Sea of Azov level”, Russian Meteorology and Hydrology, 2012, no. 37, 126–129 | DOI

[7] A. I. Sukhinov, A. E. Chistyakov, “Parallel implementation of a three-dimantional hydrodynamic model of shallow water basins on supercomputing systems”, Vychisl. Metody Programm., 13:1 (2012), 290–297

[8] L. A. Krukier, “Matematicheskoe modelirovanie gidrodinamiki Azovskogo moria pri realizatsii proektov rekonstruktsii ego ekosistemy”, Matem. model., 3:9 (1991), 3–20 | MR | Zbl

[9] http://oceanography.ru/index.php/ru/component/jdownloads/viewdownload/6-/69

[10] O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows”, Computational Mathematics and Mathematical Physics, 51:1 (2011), 160–173 | DOI | MR | Zbl

[11] O. V. Bulatov, T. G. Elizarova, “Regularized Shallow Water Equations for Numerical Simulation of Flows with a Moving Shoreline”, Comput. Math. and Mathem. Physics, 56:4 (2016), 661–679 | DOI | MR | Zbl

[12] T. G. Elizarova, D. S. Saburin, “Numerical Simulation of Fluid Oscillations in Fuel Tanks”, Mathematical Models and Computer Simulations, 5:5 (2013), 470–478 | DOI

[13] T. Elizarova, D. Saburin, “Mathematical modeling and visualization of the sloshing in the ice-breaker's tank after impact interaction with ice barrier”, Scientific Visualization, 5:4 (2014), 118–135

[14] T. G. Elizarova, M. A. Istomina, N. K. Shelkovnikov, “Numerical simulation of solitary wave generation in a wind-water annular tunnel”, Mathematical Models and Computer Simulations, 4:6 (2012), 552–559 | DOI | Zbl

[15] G. I. Marchuk, V. P. Dymnikov, V. B. Zalesny, Matematitseskie modeli v geofizitseskoi gidrodinamike i tsislennye metody ikh realizatsyi, Gigrometeoizdat, L., 1967, 296 pp. | MR

[16] N. A. Dianskii, Modelirovanie tsirkulytsyi okeana i issledovanie ego reaktsyi na korotkoperiodnye i dolgoperiodnye atmosfernye vozdeystvia, Fizmatlit, M., 2013, 271 pp.

[17] N. E. Voltsinger, R. V. Piaskjvckii, Teoria melkoi vody. Okeanologitseskie zadachi i chislennye metody, Gidrometeoizdat, L., 1977, 206 pp.

[18] T. G. Elizarova, Quasi-Gas Dynamic equations, Springer-Verlag, Berlin–Heidelberg, 2009, 286 pp. | MR | Zbl

[19] Yu. V. Sheretov, Dinamika sploshnih sred pri prostranstvenno-vremennom osrednenii, M.–Ishevsk, 2009, 400 pp.

[20] B. N. Chetverushkin, Kinetic schemes and quasi-gasdynamic system of equations, CIMNE, Barcelona, 2008

[21] A. A. Zlotnik, “Energy equalities and estimates for barotropic quasi-gasdynamic and quasi-hydrodynamic systems of equations”, Computational Mathematics and Mathematical Physics, 50:2 (2010), 310–321 | DOI | MR | Zbl

[22] Yu. V. Sheretov, Regularizovannie uravnenia gidrodinamiki, Tverskoy gos. universitet, Tver, 2016, 222 pp.