Simulation of a two-dimensional laminar boundary layer using the method «whirl in a cell»


The paper deals with the use of the «whirl in a cell» (WC) method for direct mathematical simulation of a laminar boundary layer. According to the method the processes of convection and those of diffusion both in the free flow and from the surface of the body are considered separately at each step in time. Because of the difference in velocities of diffusion and convection processes integration with different steps in time is used. The velocity profiles obtained are compared with the Blazius solution and the results of other authors. It is shown that using the «WC» method good agreement with Blazius’ results is obtained only in a certain narrow area of Reynolds’ numbers.

About the authors

1 1

Samara State Aerospace University

Author for correspondence.
Russian Federation

1 1

Samara State Aerospace University

Russian Federation


  1. Taranov A., Kornev N., Leder A. Development of the Computational Vortex Method for Calculation of Two-Dimensional Ship Sections with Flow Separation, Schiffbauforschung, 39, 2000, 2, pp. 95-105.
  2. Kornev N., Leder A., Mazaev K. Comparison of two fast algorithms for the calculation of flow velocities induced by a threedimensional vortex field, Schiffbauforschung, 40, 2001, 1, pp. 47-55.
  3. Nakamura H., Kamemoto K., Igarashi T. Analysis of unsteady heat transfer in the wake behind a circular cylinder in a uniform flow by a the Second International Conference on Vortex Methods, Sept. 26-28, Turkey, 2001, pp. 235-242.
  4. Prediction of aerodynamic sound spectra by using an advanced vortex method, Proceedings of the Second InternationalConferenceon Vortex Methods, Sept. 26-28, Turkey, 2001, pp. 235-242.
  5. Никонов В. В., Шахов В. Г. Модификация схемы «донор-акцептор» для расчета диффузии завихренности и ее применение в методе «вихрь в ячейке» // Вестник СГАУ, № 1 (3), Самара, 2003. - С. 38-46.
  6. Белоцерковский С. М., Ништ М. И. Отрывное и безотрывное обтекание тонких крыльев идеальной жидкостью. - М.: Наука, 1978.
  7. Basin M., KornevN. Beruecksichtigung der Reibung in derWirbelmethode, ZAMM, 78, 1998, 5, pp. 335-344.
  8. Справочник по прикладной статистике в 2-х т.: Под ред. Э. Ллойда, У. Ледермана. – М.: Финансы и статистика, 1989.
  9. Nikonov V., Kornev N., Leder A. The Ratio between Spatial and Time Resolutions for the Diffusion Substep in 2D Computational VortexMethods, Schiffbauforschung, 2002, vol. 41, N 3/4. pp. 5-12.
  10. Koumoutsakos P., Leonard A. Highresolution simulations of the flow around an impulsively started cylinder using vortex methods, J. Fluid Mech., 296, 1995, pp. 1-38.
  11. Cottet G.-H.,Koumoutsakos P. Vortex methods: theory and practice, Cambridge University Press, 2000.
  12. Григорьев Ю. Н., Вшивков В. А. Численные методы «частицы-в-ячейках». - Новосибирск: Наука, Сибирская издательская фирма РАН, 2000.
  13. Шлихтинг Г. Теория пограничного слоя: Пер. с нем. Г. А. Вольперта, под. ред. Лойцянского Л. Г. - М.: Наука, 1974.
  14. Wu J.C. Numerical boundary conditions for viscous flow problems, AIAA Journal, 14, 1976, pp. 104-1049.
  15. Ota S., Kamemoto K. Study on higher resolution of vorticity layer over a solid boundary for vortex methods, Proc. of The Second Intern. Conf. on Vortex Methods, Istanbul, Turkey, September 26-28, 2001, pp. 33-40.



Abstract: 2288

PDF (Russian): 1348




  • There are currently no refbacks.

Copyright (c) 2015 VESTNIK of the Samara State Aerospace University

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies