Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studia Geotechnica et Mechanica

The Journal of Wroclaw University of Technology

4 Issues per year

Open Access
See all formats and pricing
More options …

Random Vortex Method in Numerical Analysis of 2D Flow Around Circular Cylinder

Stanisław Kostecki
Published Online: 2015-02-28 | DOI: https://doi.org/10.2478/sgem-2014-0036


A combination of the vortex method and the boundary element method is used here to predict the two-dimensional flow field around a circular cylinder. Cylindrical structures experience strong hydrodynamic loading, due to vortex detachment from the both sides of cylinder during the flow. Thus, the practical meaning of such calculation is significant particularly in offshore oil and gas engineering as well as in the bridge and hydraulic structure engineering. This paper presents the mathematical formulation of the vortex method for the velocity and vorticity field calculation. The calculated velocity and vorticity fields are then used to predict the pressure distribution on the cylinder surface by the boundary element method. The resulting pressure on the cylinder, the Strouhal number and the length of the base recirculation zone are compared with solutions of other numerical methods and experiments, and a good agreement is achieved.

Keywords: vorticity; vortex method; flow instability; circular cylinder; boundary element method


  • [1] AL-JAMAL H., DALTON C., Two-dimensional numerical simulation of a wave with a current past a circular cylinder. Part 1. Inline flow, Applied Mathematical Modelling, 2013, Vol. 37, 7521-7538.Google Scholar

  • [2] CATALANO P., WANG M., IACCARINO G., MOIN P., Numerical simulation of the flow around a circular cylinder at high Reynolds numbers, Int. J. of Heat and Fluid Flow, 2003, Vol. 24, 463-469.Google Scholar

  • [3] FALLAH K., FARDAD A., FATTAHI E., SEDAGHATI ZADEH N., GHADERI A., Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers, Acta Mech., 2012, Vol. 223, 221-236.Web of ScienceGoogle Scholar

  • [4] GAUL L., KÖGL M., WAGBER M., Boundary element methods for engineers and scientists, an introductory course with advanced topics, Springer-Verlag, Berlin-Heidelberg 2003.Google Scholar

  • [5] GRESHO P.M., On Pressure Boundary Conditions for the Incompressible Navier-Stokes Equations, Int. J. Num. Meth. Fluids, 1987, Vol. 7, 1111-1145.Google Scholar

  • [6] GUILMINEAU E., QUEUTEY P., Numerical simulation of vortex- induced vibration of a circular cylinder with low massdamping in a turbulent flow, Journal of Fluids and Structures, 2004, Vol. 19, 449-466.Google Scholar

  • [7] HUANG G., HUAN H., XU X., LIU Y., Simulation of Flow Past Two Tandem Cylinders Using Deterministic Vortex Method, Thermal Science, 2012, Vol. 16, No. 5, 1460-1464.Web of ScienceCrossrefGoogle Scholar

  • [8] HUANG Y., WU W., Numerical Study Of Particle Distribution In Wake Of Liquid-Particle Flows Past A Circular Cylinder Using Discrete Vortex Method, Appl. Math. Mech., 2006, Vol. 27(4), 535-542.Google Scholar

  • [9] KOSTECKI S., Numerical Determination of the Hydrodynamic Pressure Acting on a Hydraulic Gate, Polish J. of Environ. Stud., 2007, Vol. 16, No. 6B, 39-45.Google Scholar

  • [10] KOSTECKI S., Numerical modelling of flow through moving water-control gates by vortex method. Pt. I. Problem formulation, Archives of Civil and Mechanical Engineering, 2008, Vol. VIII, No. 3, 73-89.Google Scholar

  • [11] LEWIS R.I., Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems, Cambridge University Press, London, 2005.Google Scholar

  • [12] LIANG H., ZONGA Z., ZOUB L., ZHOUA L., SUNA L., Vortex shedding from a two-dimensional cylinder beneath a rigid wall and a free surface according to the discrete vortex method, European Journal of Mechanics B/Fluids, 2014, Vol. 43, 110-119.CrossrefWeb of ScienceGoogle Scholar

  • [13] MAJDA A.J., BERTOZZI A.L., Vorticity and Incompressible Flow, Cambridge University Press, Cambridge 2002.Google Scholar

  • [14] SHADEMAN M., NOURI M., A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow Around Circular Cylinder, Journal of Computational Multiphase Flows, 2014, Vol. 6, No. 2, 151-168.Google Scholar

  • [15] SHIH W.C.L., WANG C., COLES D., ROSHKO A., Experiments on flow past rough circular cylinders at large Reynolds numbers, Journal of Wind Engineering and Industrial Aerodynamics, 1993, Vol. 49, Iss. 1-3, 351-368.Google Scholar

  • [16] STRINGER R.M., ZANG J., HILLIS A.J., Unsteady RANS computations of flow around a circular cylinder for a wide range of Reynolds numbers, Ocean Engineering, 2014, Vol. 87, 1-9.Web of ScienceCrossrefGoogle Scholar

  • [17] ZDRAVKOVICH M.M., Flow Around Circular Cylinders, Vol. 1. Fundamentals, Oxford Scientific, Oxford 1997.Google Scholar

  • [18] ZDRAVKOVICH M.M., Conceptual overview of laminar and turbulent flows past smooth and rough circular-cylinders, J. Wind Eng. Ind. Aerodyn., 1990, Vol. 33, 53-62.Google Scholar

About the article

Published Online: 2015-02-28

Citation Information: Studia Geotechnica et Mechanica, Volume 36, Issue 4, Pages 57–63, ISSN (Online) 2083-831X, ISSN (Print) 0137-6365, DOI: https://doi.org/10.2478/sgem-2014-0036.

Export Citation

© 2014 Stanisław Kostecki. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in