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Article title DEVELOPMENT OF REGULARIZED MATHEMATICAL MODEL FOR SIMULATION HYDRODYNAMICS AND SURGE PHENOMENA IN SHALLOW WATER BASINS AND ITS PARALLEL IMPLEMENTATION FOR SHRED MEMORY COMPUTER SYSTEMS
Authors A.V. Shishenya, A.I. Sukhinov
Section SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES
Month, Year 12, 2014 @en
Index UDC 519.6
DOI
Abstract In the paper we develop mathematical models for free-surface hydrodynamics simulation based on both classical Navies-Stokes equations and it’s hyperbolized analogous. We also pose adjusted boundary conditions for both models and perform discretization with finite volume method accounting fullness of the grid cells that allows us to improve precision of the obtaining results. It allows to improve the accuracy of the results, as well as to take into account the motion of the free surface and the change in the coastline due to surge phenomena. Adjusted boundary conditions are especially important for shallow water basins due to close location of horizontal boundaries, which introduce approximation errors into velocity and pressure fields inside the computational domain. The application of the created mathematical models for predicting adverse and dangerous phenomena in water media requires it’s effective parallel implementation. It could be reached by using explicit stencils when solving PDEs numerically. It is well-known that using explicit stencil imposes hard stability conditions on temporal step that’s why we suggest to use regularizer, that allows to ease this restriction. We also derived asymptotic condition of efficiency of the hyperbolized model compared to the classical one. Parallel implementation of the regularized model is performed for shared memory supercomputer system; efficiency and speed-up of the parallel program were measured.

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Keywords Hydrodynamics; free surface; shallow water basin; hyperbolized system of hydrodynamics; parallel algorithms for shared memory supercomputer systems.
References 1. Shishenya A.V. Trekhmernaya model' gidrodinamiki i protsessov perenosa tepla i soley v akvatorii Azovskogo morya s uchetom sgonno-nagonnykh yavleniy [Three-dimensional model of hydrodynamics and heat and salinity transfer in the sea of Azov taking into account wind-surge phenomena], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2011, No. 8 (121), pp. 44-57.
2. 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.
3. Sukhinov A.I., Chistyakov A.E., Timofeeva E.F., Shishenya A.V. Matematicheskaya model' rascheta pribrezhnykh volnovykh protsessov [The mathematical model of calculation of coastal wave processes], Matematicheskoe modelirovanie [Mathematical modeling], 2012, Vol. 24, No. 8, pp. 32-44.
4. Sukhinov A.I., Nikitina A.V., Chistyakov A.E. Modelirovanie stsenariya biologicheskoy reabilitatsii Azovskogo morya [The scenario modeling biological rehabilitation of the Azov sea], Matematicheskoe modelirovanie [Mathematical modeling], 2012, Vol. 24, No. 9, pp. 3-21.
5. 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, No. 5, pp. 562-574.
6. Alekseenko E., Roux B., Sukhinov A., Kotarba R., Fougere D. Nonlinear hydrodynamics in a Mediterranean lagoon, Nonlinear Processes in Geophysics, 2013, No. 20 (2), pp. 189-198.
7. Sukhinov A.I., Chistyakov A.E., E.F. Timofeeva E.F., Shishenya A.V. Mathematical model for calculating coastal wave processes, Mathematical Models and Computer Simulations, 2013, No. 5(2).
8. 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-convection-reaction, takes into the degree filling of the control volume], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2013, No. 4 (141), pp. 87-98.
9. Alekseenko E., Sukhinov A., Roux B., Kotarba R., Fougere D. coastal hydrodynamics in a windy lagoon, Computers & Fluids, 2013, Т. 77, pp. 24-35.
10. 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.
11. Chetverushkin B.N. Resolution limits of continuous media models and their mathematical formulations, Mathematical Models and Computer Simulations, 2013, Vol. 5, No. 3, pp. 266.
12. Chetverushkin B.N., Shilnikov E.V., Davydov A.A. Numerical simulation of the continuous media problems on hybrid computer systems, Advances in engineering software, 2013, Vol. 60-61, pp. 42-47.
13. Shil'nikov E.V. Modelirovanie techeniy vyazkogo gaza na osnove KGD sistemy uravneniy na neortogonal'nykh indeksnykh setkakh [Modeling of flows of viscous gas on the basis of ODG system of equations on non-orthogonal index grids], Preprinty IPM im. M.V. Keldysha [Preprints IPM M.V. Keldysh], 2014, No. 33, pp. 1-20.
14. Chetverushkin B.N., Abalakin I.V., Antonov M.A., Dorodnitsyn L.V., Elizarova T.G., Kosarev L.V., Lukshin A.V., Trapeznikova M.A., Sheretov Yu.V., Shobukhov A.V., Gurov D.B., Chayka A.S. Kineticheski-soglasovannye raznostnye skhemy gazovoy dinamiki, otchet o NIR
№ 94-01-01526 [Kinetically-consistent finite difference schemes of gas dynamics, research report No. 94-01-01526] (Rossiyskiy fond fundamental'nykh issledovaniy).
15. Sukhinov A.I., Chistyakov A.E. Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator, Nonlinear Processes in Geophysics, 2013, No. 20 (2), pp. 189-198.
16. Sukhinov A.I., Shishenya A.V. Increasing efficiency of alternating triangular method based on improved spectral estimates, Mathematical Models and Computer Simulations, 2013, No. 5(3).
17. Sukhinov A.I., Shishenya A.V. Uluchshenie otsenki parametra γ1 poperemenno-treugol'nogo iteratsionnogo metoda s apriornoy informatsiey [Improvement etimation of γ1 for ssor with a priori information], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2010, No. 6 (107), pp. 7-15.
18. Trapeznikova M.A., Chetverushkin B.N., Churbanova N.G., Morozov D.N. A kinetically based algorithm for porous medium flow simulation on multicore computer systems, ECCOMAS 2012 – European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers 2012, pp. 2702-2708.
19. Chetverushkin B.N., Davydov A.A., Shil'nikov E.V. Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems, Computational Mathematics and Mathematical Physics, 2010, Vol. 50, No. 12, pp. 2157-2165.

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