|Article title||TIME-CONSUMING COMPARISON OF EXPLICIT AND IMPLICIT SCHEMES FOR NUMERICAL REALIZATION OF THE SEDIMENT TRANSPORT PROBLEM IN COASTAL SYSTEMS|
|Authors||E.A. Protsenko, A.E. Chistyakov, S.A. Shreter, A.A. Sukhinov|
|Section||SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES|
|Month, Year||12, 2014 @en|
|Abstract||For reliable prediction of dynamic phenomena of the coastal zone there is a need to construct mathematical models of transport of matter in shallow water under the influence of surface gravity waves, which play an important role in the prediction of possible intervention into the ecosystem, in the analysis of the current situation in the operational decisions on overcoming of anthropogenic influences. The purpose of work consists in the creation and implementation of a two-dimensional continuous and discrete models of transport of deposits in the coastal water systems, describing the rearrangement of the coastal zone of the reservoirs due to the movement of water and solid particles and satisfying the basic conservation laws. For the solution of the problem were used both traditional (implicit), and explicit discrete models, with addition in the last of regularized according to B.N. Chetverushkin composed – discrete analog of a differential derivative of the second order on time. The spatial three-dimensional model of hydrodynamics in the coastal zone of reservoirs and model of the transport of suspended particles were built and implemented on a cluster of distributed computing. The results of numerical experiments are given. The main aim of this work is to compare the time costs for algorithms based on traditional implicit and explicit regularization schemes. In work the choice of admissible value of a multiplier at a differential derivative of the second order is considered – a scheme regulyarizator which is necessary for creation of effective parallel algorithm of the solution of this task on systems with mass overlapping. Developed numerical algorithms and implementing them complex programs have practical significance: they can be used for studies of hydrophysical processes in the coastal water systems, testing hypotheses and predicting the dynamics of the bottom region of shallow water bodies and shorelines. The findings will improve existing models to predict changes in the underwater topography and shape of the coastline.|
|Keywords||Parallel computing; sediment transport; discrete model; difference equations; numerical experiment; method of regularization; implicit schemes.|
|References||1. Leont'ev I.O. Pribrezhnaya dinamika: volny, techeniya, potoki nanosov [Coastal dynamics: waves, currents, sediment flow]. Moscow: Geos., 2001, 272 p.
2. Protsenko E.A. Model' i algoritmy resheniya zadachi o transporte nanosov [Model and algorithms for solving the problem of sediment transport], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2009, No. 8 (97), pp. 71-75.
3. Protsenko E.A. Dvumernaya konechno-raznostnaya model' formirovaniya nanosov v pribrezhnoy zone vodoema i ee programmnaya realizatsiya [Two-dimensional finite-difference
model of the formation of sediment in the coastal zone of the reservoir and its software implementation], Inzhenernyy vestnik Dona [Engineering Journal of Don], 2010, Vol. 13, No. 3, pp. 23-31.
4. Sukhinov A.I., Chistyakov A.E., Protsenko E.A. Mathematical modeling of sediment transport in the coastal zone of shallow reservoirs, Mathematical Models and Computer Simulations, 2014, Vol. 6, Issue 4, pp. 351-363.
5. Sukhinov A.I., Chistyakov A.E., Protsenko E.A. Matematicheskoe modelirovanie transporta nanosov v pribrezhnykh vodnykh sistemakh na mnogoprotsessornoy vychislitel'noy sisteme
[Mathematical modeling of sediment transport in coastal aquatic systems on a multiprocessor computer system] Vychislitel'nye metody i programmirovanie [Computational methods and
programming], 2014, Vol 15, pp. 610-620.
6. Ezer T., Mellor G.L. Sensitivity studies with the North Atlantic sigma coordinate Princeton Ocean Model, Dynamics of Atmospheres and Oceans, 2000, Vol. 32, pp. 155-208.
7. Degtyareva E.E., Protsenko E.A., Chistyakov A.E. Programmnaya realizatsiya trekhmernoy matematicheskoy modeli transporta vzvesi v melkovodnykh akvatoriyakh [A software implementation of a three-dimensional mathematical model of the transport of sediment in the shallow waters of the], Inzhenernyy vestnik Dona [Engineering Journal of Don], 2012, Vol. 23, No. 4-2, pp. 30.
8. Degtyareva E.E., Chistyakov A.E. Modelirovanie transporta nanosov po dannym eksperimental'nykh issledovaniy v Azovskom more [Modeling sediment transport based on experimental studies in Azov sea], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU.
Engineering Sciences], 2012, No. 2 (127), pp. 112-118.
9. Sukhinov A.I., Nikitina A.V., Chistyakov A.E., Semenov I.S. Matematicheskoe modelirovanie usloviy formirovaniya zamorov v melkovodnykh vodoemakh na mnogoprotsessornoy
vychislitel'noy sisteme [Mathematical modeling of the formation of Zamora in shallow waters on a multiprocessor computer system], Vychislitel'nye metody i programmirovanie [Computational methods and programming], 2013, Vol. 14, pp. 103-112.
10. Sukhinov A.I., Nikitina A.V. Matematicheskoe modelirovanie i ekspeditsionnye issledovaniya kachestva vod v Azovskom more [Mathematical modelling and expeditional investigations of
water quality in Azov sea], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2011, No. 8 (121), pp. 62-73.
11. Sukhinov A.I., Chistyakov A.E., Fomenko N.A. Metodika postroeniya raznostnykh skhem dlya zadachi diffuzii-konvektsii-reaktsii, uchityvayushchikh stepen' zapolnennosti kontrol'nykh yacheek [Method of construction difference scheme for problems of diffusion-convectionreaction, takes into the degree filling of the control volume] Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 4 (141), pp. 87-98.
12. 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,
Mathematical Models and Computer Simulations, 2011, Vol. 3, Issue 5, pp. 562-574.
13. Vasil'ev V.S., Sukhinov A.I. Pretsizionnye dvumernye modeli melkikh vodoemov [Precision two-dimensional model of shallow pools], Matematicheskoe modelirovanie [Mathematical
modeling], 2003, Vol. 15, No. 10, pp. 17-34.
14. Sukhinov A. I., Chistyakov A. E., Timofeeva E. F., Shishenya A. V Mathematical model for calculating coastal wave processes, Mathematical Models and Computer Simulations, 2013, Vol. 5, Issue 2, pp. 122-129.
15. Chistyakov A.E. Ob approksimatsii granichnykh usloviy trekhmernoy modeli dvizheniya vodnoy sredy [On approximation of the boundary conditions of the three-dimensional model of water environment], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2010, No. 6 (107), pp. 66-77.
16. Chetverushkin B.N. Predely detalizatsii i formulirovka modeley uravneniy sploshnykh sred [The limits of detail and formulation of the model equations of continuous media], Matematicheskoe modelirovanie [Mathematical modeling], 2012, Vol. 24, No. 11, pp. 33-52.
17. Sukhinov A. I., Chistyakov A. E., Shishenya A. V. Error estimate for diffusion equations solved by schemes with weights, Mathematical Models and Computer Simulations, 2014, Vol. 6, Issue 3, pp. 324-331.
18. Samarskiy A.A. Teoriya raznostnykh skhem [The theory of difference schemes]. Moscow: Nauka, 1989, 432 p.
19. Samarskiy A.A., Nikolaev E.S. Metody resheniya setochnykh uravneniy [Methods for solving grid equations]. Moscow: Nauka, 1978, 532 p.
20. Konovalov A.N. The steepest descent method with an adaptive alternating-triangular preconditioner, Differential Equations, 2004, pp. 1018-1028.
21. Konovalov A.N. To the Theory of the Alternating Triangle Iteration Method, Siberian Mathematical Journal, 2002, Vol. 43, Issue 3, pp. 439-457.
22. Sukhinov A. I., Chistyakov A. E. Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator, Mathematical Models and Computer Simulations, 2012, Vol. 4, Issue 4, pp. 398-409.
23. Chistyakov A.E. Teoreticheskie otsenki uskoreniya i effektivnosti parallel'noy realizatsii PTM skoreyshego spuska [Speedup and efficiency estimation of parallel SSOR algorithm], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2010, No. 6 (107), pp 237-249.
24. Tipovaya tekhnologicheskaya skhema dobychi peska, graviya i peschano-graviynoy smesi sudokhodnykh rek i drugikh vodoemov [Typical technological scheme of production of sand, gravel and sand-gravel aggregate shipbuilding output of the rivers and other water bodies]. Moscow: Transport, 1980.