Skip Navigation

Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 17027, 31 pages, doi:10.1155/AMRX/2006/17027
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Giovannini, A.
Right arrow Articles by Gagnon, Y.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Validation of a three-dimensional vortex particle method for fluid flows

André Giovannini and Yves Gagnon

Institut de Mécanique des Fluides de Toulouse, Université Paul Sabatier avenue du Professeur Camille Soula, 31400 Toulouse, France E-mail address: andre.giovannini{at}imft.fr
Chaire K.-C.- Irving en Développment Durable, Université de Moncton Moncton, NB, Canada E1A 3E9 E-mail address: gagnony{at}umoncton.ca

In the context of complex vortex dynamics and interactions studies, an algorithm based on vortex particle methods is developed while a set of validation tests and a detailed comparison with a pseudospectral code are presented. The two physical problems considered are the isolated Lamb-Oseen tube (case A) and the antiparallel tubes (Crow instability, case B). The objectives of the work are to quantify the influence of the temporal and the spatial resolutions on the solution, to evaluate the numerical diffusion, and to look at the robustness and the ability of the algorithm to handle small tubular scales at a maximum Reynolds number. Finally, for the so-called Crow instability (case B), comparisons between the vortex-in-cell algorithm at 64, 128, and 256 spatial resolutions are carried out with a spectral method, for a Reynolds number of 1500. The results contribute to a better knowledge of the stability, accuracy, and dissipative behaviour of 3D vortex methods for modelling fluid flows.



References

  1. Anderson C. R. An implementation of the fast multipole method without multipoles. SIAM Journal on Scientific and Statistical Computing (1992) 13(4):923–947.[CrossRef][Web of Science]
  2. Ashurst W. T., Meiburg E. Three-dimensional shear layers via vortex dynamics. Journal of Fluid Mechanics (1988) 189:87–116.[CrossRef][Web of Science]
  3. Beale J. T., Majda A. Rates of convergence for viscous splitting of the Navier-Stokes equations. Mathematics of Computation (1981) 37(156):243–259.[CrossRef][Web of Science]
  4. Beale J. T., Majda A. Vortex methods. II. Higher order accuracy in two and three dimensions. Mathematics of Computation (1982) 39(159):29–52.[CrossRef][Web of Science]
  5. Brancher P., Chomaz J. M., Huerre P. Direct numerical simulations of round jets: vortex induction and side jets. Physics of Fluids (1994) 6(5):1768–1774.[CrossRef][Web of Science]
  6. Chorin A. J. Numerical study of slightly viscous flow. Journal of Fluid Mechanics (1973) 57(4):785–796.[CrossRef]
  7. Chorin A. J. Vortex sheet approximation of boundary layers. Journal of Computational Physics (1978) 27(3):428–442.[CrossRef][Web of Science]
  8. Christiansen I. P. Numerical simulation of hydrodynamics by the method of point vortices. Journal of Computational Physics (1973) 13(3):363–379.[CrossRef][Web of Science]
  9. Cottet G.-H., Koumoutsakos P. D. Vortex Methods. Theory and Practice (2000) Cambridge: Cambridge University Press. xiv+313.
  10. Crow S. C. Stability theory for a pair of trailing vortices. AIAA Journal (1970) 8(12):2172–2179.
  11. Degond P., Mas-Gallic S. The weighted particle method for convection-diffusion equations. I. The case of an isotropic viscosity. Mathematics of Computation (1989) 53(188):485–507.[CrossRef][Web of Science]
  12. Degond P., Mas-Gallic S. The weighted particle method for convection-diffusion equations. II. The anisotropic case. Mathematics of Computation (1989) 53(188):509–525.[CrossRef][Web of Science]
  13. El Hamraoui M. Contribution à la simulation d'écoulement tridimensionnel par methode de vortex (1999) Toulouse III: Université Paul Sabatier.
  14. Gagnon Y., Cottet G.-H., Dritschel D. G., Ghoniem A. F., Meiburg E., eds. Vortex Flows and Related Numerical Methods. II. In: European Series in Applied and Industrial Mathematics Proceedings (1996) 1. Paris: Société de Mathématiques Appliquées et Industrielles. v+585.
  15. Giovannini A., Cottet G.-H., Gagnon Y., Ghoniem A. F., Meiburg E., eds. Flows and Related Numerical Methods. In: European Series in Applied and Industrial Mathematics Proceedings (1999) 7. Paris: Société de Mathématiques Appliquées et Industrielles.
  16. Greengard L., Rokhlin V. A fast algorithm for particle simulations. Journal of Computational Physics (1987) 73(2):325–348.[CrossRef][Web of Science]
  17. Jeong J., Hussain F. On the identification of a vortex. Journal of Fluid Mechanics (1995) 285:69–94.[CrossRef][Web of Science]
  18. Kida S., Takaoka M. Reconnection of vortex tubes. Fluid Dynamics Research (1988) 3(1–4):257–261.[CrossRef]
  19. Knio O. M., Klein R. Improved thin-tube models for slender vortex simulations. Journal of Computational Physics (2000) 163(1):68–82.[CrossRef][Web of Science]
  20. Leonard A. Computing three-dimensional incompressible flows with vortex elements. Annual Review of Fluid Mechanics (1985) 17:523–559.[CrossRef][Web of Science]
  21. Lesieur M., Comte P., Lamballais E., Métais O., Silvestrini G. Large-eddy simulations of shear flows. Journal of Engineering Mathematics (1997) 32(2-3):195–215.[Medline]
  22. Margerit D., Brancher J.-P. Asymptotic expansions of the Biot-Savart law for a slender vortex with core variation. Journal of Engineering Mathematics (2001) 40(3):297–313.[CrossRef][Web of Science]
  23. Marshall J. S., Brancher P., Giovannini A. Interaction of unequal anti-parallel vortex tubes. Journal of Fluid Mechanics (2001) 446:229–252.[Web of Science]
  24. Marzouk Y. M., Ghoniem A. F. K-means clustering for optimal partitioning and dynamic load balancing of parallel hierarchical N-body simulations. Journal of Computational Physics (2005) 207(2):493–528.[CrossRef][Web of Science]
  25. Melander M. V., Hussain F. Cross-linking of two antiparallel vortex tubes. Physics of Fluids A (1989) 1(4):633–636.[CrossRef]
  26. Monaghan J. J. Extrapolating B-splines for interpolation. Journal of Computational Physics (1985) 60(2):253–262.[CrossRef][Web of Science]
  27. Ould-Sahili M. L. Couplage de methodes numériques en simulation directe d'ecoulements incompressibles (1998) Grenoble: Université Joseph Fourier.
  28. Ould-Salihi M. L., Cottet G.-H., El Hamraoui M. Blending finite-difference and vortex methods for incompressible flow computations. SIAM Journal on Scientific Computing (2000) 22(5):1655–1674.[CrossRef][Web of Science]
  29. Persillon H., Braza M. Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation. Journal of Fluid Mechanics (1998) 365:23–88.[CrossRef][Web of Science]
  30. Rebach C. Numerical calculation of 3D unsteady flows with vortex sheets. (1978) AIAA Paper 111.
  31. Robinson S. K. Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics (1991) 23:601–639.[CrossRef][Web of Science]
  32. Saffman P. G. Vortex Dynamics. In: Cambridge Monographs on Mechanics and Applied Mathematics (1992) New York: Cambridge University Press. xii+311.
  33. Saghbini J. C., Ghoniem A. F. Numerical simulation of the dynamics and mixing in a swirling flow. (1997) AIAA Paper 97-0507.
  34. Thompson M. C., Hourigan K., Sheridan J. Three dimensional instabilities in the wake of a circular cylinder. International Journal of Experimental Heat Transfer, Thermodynamics, and Fluid Mechanics (1996) 12:190–196.
  35. Winckelmans G. S., Leonard A. Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows. Journal of Computational Physics (1993) 109(2):247–273.[CrossRef][Web of Science]
  36. Winckelmans G. S., Salmon J. K., Warren M. S., Leonard A., Jodoin B. Application of fast parallel and sequential tree codes to computing three-dimensional flows with the vortex element and boundary element methods. In: ESAIM Proceedings (1996) 1. Vortex Flows and Related Numerical Methods, II, 1995: Montreal, PQ. Paris: Société de Mathématiques Appliquées et Industrielles. 225–240.

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Giovannini, A.
Right arrow Articles by Gagnon, Y.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?