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Numerical Analysis of the Problem of Flow Past a Cylindrical Body Applying the R-Functions Method and The Galerkin Method

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EN
Abstrakty
EN
The article considers the stationary problem of viscous incompressible fluid flow past a cylindrical body. For solving the problem it is proposed a numerical method, based on the joint use of R-functions method and the Galerkin method. The computational experiment has been conducted for the task of flow past square cylinder for different Reynolds numbers.
Twórcy
  • Department of Applied Mathematics, Kharkiv National University of Radio Electronics, Lenina Av. 14, Kharkiv, 61166, Ukraine
  • Department of Advanced Mathematics, O.M. Beketov National University of Urban Economy in Kharkiv, Revolutsii Street 12, Kharkiv, 61002, Ukraine
  • Department of Applied Mathematics, Kharkiv National University of Radio Electronics, Lenina Av. 14, Kharkiv, 61166, Ukraine
Bibliografia
  • 1. Babenko K.I., Vvedenskaya N.D. and Orlova M.G. 1975. Calculation of the steady flow of a viscous fluid past a circular cylinder (in Russian). Zh. vychisl. mat. i mat. fiz., 15 (№ 1), 183-196.
  • 2. Batluk V., Basov M. and Klymets’. 2013. Mathematical model for motion of weighted parts in curled flow. ECONTECHMOD An International Quarterly Journal On Economics In Technology, New Technologies And Modelling Processes. Vol. 2, No 3, 17-24.
  • 3. Batluk V. and Batluk V. 2012. Scientific bases of creation of dust catchers. ECONTECHMOD An International Quarterly Journal On Economics In Technology, New Technologies And Modelling Processes. Vol. 1, No 4, 3-7.
  • 4. Batluk V., Batluk V., Basov M. and Dorundyak L. 2012. Mathematic model of the process of dust catching in an apparatus with a movable separator. ECONTECHMOD An International Quarterly Journal On Economics In Technology, New Technologies And Modelling Processes. Vol. 1, No 1, 13-16.
  • 5. Happel J. and Brenner H. 1965. Low Reynolds Number Hydrodynamics: with special applications to particulate media. Prentice-Hall, 630.
  • 6. Kolosova S.V. 1972. The use of projection methods and R-functions method to the solution of boundary value problems in infinite domains (in Russian). PhD thesis, Kharkiv National University of Radioelectronics, 85.
  • 7. Kolosova S.V., Lamtyugova S.N. and Sidorov M.V. 2003. The iterative methods application to solving the external tasks of hydrodynamics (in Russian). Radioelektronica i informatika, № 3, 13-17.
  • 8. Kolosova S.V. and Sidorov M.V. 2003. Application of R-functions method to the calculation of plane viscous liquid flows (in Russian). Vestnik KhNU. Ser. Prykl. Math. And Mech., № 602, 61-67.
  • 9. Kravchenko V.F. and Rvachev V.L. 2006. The algebra of logic, atomic functions and wavelets (in Russian). Moscow: Fizmatlit, 400.
  • 10. Krasnoselskiy M.A., Vainikko G.M., Zabreiko P.P., Rutitskii Y.B. and Stecenko V.Y. 1969. Approximate solution of operator equations (in Russian). Moscow: Nauka, 420.
  • 11. Kutepov A.M., Polyanin A.D., Zapryanov Z.D., Vyazmin A.V. and Kazenin D.A. 1996. Chemical Hydrodynamics (Handbook) (in Russian). Moscow: Quantum, 336.
  • 12. Lamb H. 1993. Hydrodynamics. 6th Edition. Cambridge University Press, 768.
  • 13. Lamtyugova S.N. 2012. Mathematical modelling of flow linearized problems in the spherical and cylindrical coordinate systems (in Russian). Visnyk ZNU. Physics Mathematics, № 1, 112-122.
  • 14. Lamtyugova S.N. 2012. Mathematical modeling of steady flow past a cylindrical body with viscous fluid (in Russian). Visnyk ZNU. Physics Mathematics, № 2, 57-65.
  • 15. Lamtyugova S.N. 2012. The R-functions method application to solving mass transfer problems. Proceedings of the 2nd international scientific conference of students and young scientists. Theoretical and applied aspects of cybernetics. Kyiv: Bukrek, 108-111.
  • 16. Landau L.D. and Lifshitz E.M. 1987. Fluid Mechanics. 2 Ed. Volume 6 of Course of Theoretical Physics. Pergamon Press, 532.
  • 17. Loitsyansky L.G. 1995. Mechanics of Liquids and Gases. 6th ed. New York: Begell House, 971.
  • 18. Maksimenko-Sheiko K.V. 2005. Mathematical modeling of heat transfer at motion of fluid through the channels with the screw type symmetry of the R-functions method (in Russian). Dop. NAN Ukr, № 9, 41-46.
  • 19. Polyanin A.D. 2001. Handbook of Linear Partial Differential Equations (in Russian). Moscow: Fizmatlit, 576.
  • 20. Polyanin A.D., Kutepov A.M., Vyazmin A.V., Kazenin.D.A. 2002. Hydrodynamics, Mass and Heat Transfer in Chemical Engineering. London: Taylor & Francis, 406.
  • 21. Polyanin A.D. and Zaitsev V.F. 2002. Handbook of Nonlinear Partial Differential Equations: Exact solutions (in Russian). Moscow: Fizmatlit, 432.
  • 22. Rvachev V.L. 1982. Theory of R-functions and its some applications (in Russian). Kiev: Nauk. Dumka, 552.
  • 23. Rvachev V.L. and Sheiko T.I. 1995. R-functions in boundary value problems in mechanics. Appl. Mech. Rev, 48(4), 151-188.
  • 24. Shapiro V. 2007. Semi-Analytic Geometry with R-Functions. Acta Numerica, 16, 239-303.
  • 25. Shkadov V.Y. and Zapryanov Z.D. 1984. Viscous Fluid Flows (in Russian). Moscow, 200.
  • 26. Sliozkin N.A. 1955. Dynamics of viscous incompressible fluid (in Russian). Moscow, 521.
  • 27. Strel'chenko A.J., Kolosova S.V. and Rvachev V.L. 1972. A method for solving boundary value problems (in Ukrainian). Dop. AN URSR. Ser. A, № 9, 837-839.
  • 28. Suvorova I.G. 2004. Computer modeling of axisymmetric flows in the channels of complex shape (in Russian). Vestnik NTU KhPI, № 31, 141-148.
  • 29. Suvorova I.G., Kravchenko O.V. and Baranov I.A. 2011. Mathematical and computer modeling of axisymmetric flows of incompressible viscous fluid with the use of R-function method (in Russian). Math. methody ta phys.-mech. polya, 54(2), 139-149.
  • 30. Tevyashev A.D., Gibkina N.V., Sidorov M.V. 2007. On one approach to the mathematical modeling of plane steady flows of viscous incompressible fluid in simply connected domains (in Russian). Radioelectronika i informatika, № 2, 50-57.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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