On the effective numerical methods of solution of shallow water problem. Realization of the model for the easternmost part of the Black Sea

Article Sidebar

Cover

Main Article Content

Avtandil A.Kordzadze, Demuri I.Demetrashvili,Vepkhia G.Kukhalashvili

Abstract

Two versions of the numerical method of solution of a shallow water equation system based on the two-cycle splitting method with realization for the easternmost water area of the Black Sea are presented. In the first version solution of the equation system, which is received as a result of splitting of the basic equation system with respect to physical processes (adaptation stage), is carried out with use of factorization method regarding to current velocity components. In the second version the equation system received on the adaptation stage is reduced to the oscillation equations of string, which are also solved by factorization method. The algorithms considered in the present paper do not require use of iterative methods, which considerably increase machine time for realization of a task.
PDF
Published: Apr 24, 2013

Article Details

How to Cite
Demuri I.Demetrashvili,Vepkhia G.Kukhalashvili, A. A. (2013). On the effective numerical methods of solution of shallow water problem. Realization of the model for the easternmost part of the Black Sea. Journals of Georgian Geophysical Society, 15, 14–31. Retrieved from https://ggs.openjournals.ge/index.php/GGS/article/view/45
Issue
Vol. 15: PHYSICS OF ATMOSPHERE, OCEAN AND SPACE PLASMA
Section
Articles
PKPApplication::getCCLicenseBadge(https://creativecommons.org/licenses/by-nc/4.0)

References

Marchuk G. I., Kagan B. A. Ocean tide. Leningrad, Gidrometeoizdat, 1977, 266 p (in Russian).

Backhaus J. Entwicklung eines numerischen modells zur reproduktion widangeregter

bewegungsvorgo-nge in Flash-wassergebieten mit beweglichem Rand.-Diplomarbeit. Univ.

Hmburg, 1975, 81 p.

Cherkasov L. V. Hydrodynamics of surface and internal waves. Kiev, “Naukova dumka“, 1976,

p (in Russian).

Marchuk G. I., Dymnikov V. P., Zalesny V. B. Mathematical models of geophysical

hydrodynamics and numerical methods of their realization. Leningrad, Gidrometeoizdat, 1987,

p (in Russian).

Girgvliani A. G. On numerical modeling of shallow water problems. Preprint N454, Novosibirsk, VC CO AH CCCP, 1983, 18 p (in Russian).

Kordzadze A. A. Mathematical questions of solution of ocean dynamics problems. VC CO AH

CCCP, Novosibirsk, 1982, 148 p (in Russian).

Bubnov M. A. Mathematical questions of modeling of tide and circulations in the baroclinic

ocean. VC CO AH CCCP, Novosibirsk, 1984, 152 p (in Russian).

Marchuk G. I. Methods of computer mathematics. Moscow, Nauka Press, 1977, 454 p (in

Russian).

Marchuk G. I. Numerical solution of problems of atmospheric and oceanic dynamics.

Leningrad, Gidrometeoizdat, 1974, 303 p 90 (in Russian).

Kordzadze A. A. Mathematical modeling of dynamics of sea currents ( theory, algorithm,

Numerical experiments), Moscow, OVM AH CCCP, 1989, 218 p (in Russian).

Ilin V. P., Kordzadze A. A. About one iteration scheme of a splitting method for stationary tasks of ocean currents. In: methods of computing and applied mathematics. Differential and Integral equations. VC CO AH CCCP, Novosibirsk, 1977, pp.136-146 (in Russian).

Zilitinkevich S. S., Monin A. S. Turbulence in dynamic models of the atmosphere. Nauka,

Leningrad, 1971, 41 p (in Russian).

Kordzadze A. A, Demetrashvili D. I. Operational forecast of hydrophysical fields in the Georgian Black Sea coastal zone within the ECOOP. Ocean Science, 2011, 7, pp. 793- 803, www.ocean-sci.net/7/793/2011/, doi: 10.5194/os-7-793-2011.

Kordzadze A. A, Demetrashvili D. I. Operational regional forecasting system of state of the east part of the Black Sea. Ecological safety of coastal and shelf zones and comprehensive use of shelf resources. Collected scientific papers. Sevastopol, Iss. 25, vol.2, 2011, pp.136-146 (in Russian).

Kordzadze A. A, Demetrashvili D. I., Kukhalashvili V. G. Circulation processes in the easternmost part of the Black Sea in 2010-2012. Results of circulation and forecast. J. Georgian Geoph. Soc., 2012 (in present journal).

Korotaev G. K., Oguz T., Dorofeev V. L. et al. Development of Black Sea nowcasting and orecasting system, Ocean Science, 7, 2011, P. 629-649, doi: 10.5194/os-7-629-2011.

Kubryakov A. I., Korotaev G. K., Dorofeev V. L. et al. Black Sea Coastal forecasting system. Ocean Science, 8, 2012, P. 183-196, doi: 10.5194/os-8-183-2012.