Abstract
The problem of a stationary viscous incompressible fluid flow around the cylinder has been analyzed by means of the asymptotic methods. The fluid flow equations in the variables “stream function-a vortex” are considered. One component of a vortex vector has remained in case of two-dimensional motion. Having applied the matching method the vortex asymptotics has been investigated in an interface near the cylinder. The equation of an interior boundary layer for stream function has been made with the help of using the method of matched asymptotic expansions and a matching condition with the solution for vortex. The received equation is investigated by means of numerical methods for great values of Reynolds number.
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References
Afendikov, A.L., Babenko, K.I.: Mathematical modelling of turbulence in flows of a viscous incompressible fluid (Russia). Math. Model. Moscow 1(8), 45–74 (1989)
Akhmetov, R.G.: About a matching method in the problem of viscous fluid flow around a cylinder (Russia). In: Theory of Functions, Its Applications and Related Issues. Proceedings of International Conference, 22–28 Aug 2013. Proceedings of the Mathematical Center of N.I. Lobachevsky, vol. 46, pp. 106–108. Kazan University, Kazan (2013)
Akhmetov, R.G., Kutluev, R.R.: About vortex structure at the cylinder flow viscous fluid (Russia). In: Fluxes and Structures in Fluids. Proceedings of International Conference, pp. 10–13, 25–28 June 2013. MAKS Press, Saint-Petersburg (2013)
Arnold, V.I.: Additional Chapters of the Theory of the Ordinary Differential Equations (Russia). Nauka, Moscow (1978)
Babenko K.I., Vvedenskaya N.D., Orlova M.G.: Calculation of the steady flow of a viscous fluid past a circular cylinder. Zhurnal Vychislitel’noi Matematiki and Matematicheskoi Fiziki 15(1), 183–196 (1975) [Translate from Russian to English in USSR Comput. Math. Math. Phys. 15(1), 176–190 (1975)]
Dynnikova, G.Ya.: Calculation of flow around a circular cylinder on the basis of two-dimensional Navier-Stokes equations at large Reynolds numbers with high resolution in a boundary layer. Doklady Akad. Nauk 422(6), 755–757 (2008) [Translate from Russian to English in Doklady Phys. 53(10), 544–547 (2008)]
Dynnikova, G.Ya.: Fast technique for solving the N-body problem in flow simulation by vortex methods. Zhurnal Vychislitel’noi Matematiki and Matematicheskoi Fiziki 49(8), 1458–1465 (2009) [Translate from Russian to English in Comput. Math. Math. Phys. 49(8), 1389–1396 (2009)]
Gupalo, Yu.P., Polyanin, A.D., Ryazantzev, Yu.S.: Mass and Heat Exchange of Reactive Particles with the Flow (Russia). Nauka, Moscow (1985)
Hairer, E., Norsett, S.P., Wanner, G.: Solving Ordinary Differential Equations, Nonstiff Problems. Springer, Berlin (1987)
Krasnikov, Yu.G., Solovyev, V.R.: Finding of approximate analytical solutions of the equations of Navier-Stokes for a stationary flow of the cylinder incompressible liquid (Russia). News Acad. Sci. Mech. Liquid Gas 4, 22–33 (1999)
Ladyzhenskaya, O.A.: Mathematical Problems of the Dynamics of a Viscous Incompressible Fluid (Russia). Nauka, Moscow (1970)
Ladyzhenskaya, O.A.: Sixth Problem of the Millennium: Navier–Stokes Equations, Existence and Smoothness, vol. 58(2), pp. 45–78. Uspekhi Matematicheskikh Nauk, Moscow (2003) [Translate from Russian to English in Russian Math. Surv. 58(2), 251–286 (2003)]
Lamb, G.: Hydrodynamics. Gostekhizdat, Moskow (1947) [English original text in Cambridge University Press, New York (1932)]
Loytsyansky, L.G.: Mechanics of liquids and gases (Russia). Bustard, Moskow (2003)
Van Dyke, M.: Perturbation methods in fluid mechanics. World, Moskow (1967) [English original text in Academic Press, New York (1964)]
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Akhmetov, R.G., Kutluev, R.R. (2014). Vortex Structure Around the Cylinder at a Flow of Viscous Fluid. In: Awrejcewicz, J. (eds) Applied Non-Linear Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-319-08266-0_11
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DOI: https://doi.org/10.1007/978-3-319-08266-0_11
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