Comptes Rendus
no. 4-5
Vortex methods and their application to trailing wake vortex simulations
[Les méthodes vortex et leur application à la simulation des sillages tourbillonnaires]
Grégoire Winckelmans1  ; Roger Cocle1  ; Louis Dufresne1  ; Raphaël Capart1
1 Université catholique de Louvain (UCL), Mechanical Engineering Department, Division TERM and Center for Systems Engineering and Applied Mechanics (CESAME), 1348 Louvain-la-Neuve, Belgium
Comptes Rendus. Physique, Volume 6 (2005) no. 4-5, pp. 467-486.

Les méthodes vortex sont compétitives pour la simulation d'écoulements incompressibles et instationnaires, car elles ont peu de dispersion et de bonnes propriétés de conservation de l'énergie. Les diverses méthodes sont présentées, incluant les développements récents : redistribution des particules, diffusion, relaxation (par projection), solveurs efficaces (méthode multipole rapide, méthode particules-grille, méthode hybride) et implémentation sur ordinateurs parallèles. Des examples sont présentés concernant l'application aux sillages tourbillonnaires d'ailes/avions : 2-D et 3-D, non-visqueux et visqueux, simulation directe et simulation des grandes échelles. On considère des enroulements, de la dynamique de tubes tourbillon, des instabilités 3-D et la complexité/turbulence qu'elles produisent. Un système de tourbillons en effet de sol est aussi présenté.

Vortex methods are competitive for simulating incompressible unsteady flows, because they have negligible dispersion error and good energy conservation. The various methods are presented, including the recent developments: particle redistribution, diffusion, relaxation (by projection), efficient solvers (fast multipole method, vortex-in-cell method, hybrid method) and parallel computer implementations. Examples relating to wing/aircraft trailing wake vortices are presented: 2-D and 3-D, inviscid and viscous, direct numerical simulation and large eddy simulation. We consider wake roll-ups, vortex tube dynamics, 3-D instabilities and the complexity/turbulence they produce. A vortex system in ground effects is also presented.

Publié le :
DOI : 10.1016/j.crhy.2005.05.001
Keywords: Lagrangian methods, Vortex particle methods, Vortex-in-cell methods, Unsteady flows, Turbulent flows, Direct numerical simulation, Large-eddy simulation
Mot clés : Méthodes lagrangiennes, Méthodes de particules tourbillon, Méthodes particules-grille, Écoulements instationnaires, Écoulements turbulents, Simulation numérique directe, Simulation des grandes échelles
Grégoire Winckelmans 1 ; Roger Cocle 1 ; Louis Dufresne 1 ; Raphaël Capart 1

1 Université catholique de Louvain (UCL), Mechanical Engineering Department, Division TERM and Center for Systems Engineering and Applied Mechanics (CESAME), 1348 Louvain-la-Neuve, Belgium 
@article{CRPHYS_2005__6_4-5_467_0,
     author = {Gr\'egoire Winckelmans and Roger Cocle and Louis Dufresne and Rapha\"el Capart},
     title = {Vortex methods and their application to trailing wake vortex simulations},
     journal = {Comptes Rendus. Physique},
     pages = {467--486},
     publisher = {Elsevier},
     volume = {6},
     number = {4-5},
     year = {2005},
     doi = {10.1016/j.crhy.2005.05.001},
     language = {en},
}
TY  - JOUR
AU  - Grégoire Winckelmans
AU  - Roger Cocle
AU  - Louis Dufresne
AU  - Raphaël Capart
TI  - Vortex methods and their application to trailing wake vortex simulations
JO  - Comptes Rendus. Physique
PY  - 2005
SP  - 467
EP  - 486
VL  - 6
IS  - 4-5
PB  - Elsevier
DO  - 10.1016/j.crhy.2005.05.001
LA  - en
ID  - CRPHYS_2005__6_4-5_467_0
ER  - 
%0 Journal Article
%A Grégoire Winckelmans
%A Roger Cocle
%A Louis Dufresne
%A Raphaël Capart
%T Vortex methods and their application to trailing wake vortex simulations
%J Comptes Rendus. Physique
%D 2005
%P 467-486
%V 6
%N 4-5
%I Elsevier
%R 10.1016/j.crhy.2005.05.001
%G en
%F CRPHYS_2005__6_4-5_467_0
Grégoire Winckelmans; Roger Cocle; Louis Dufresne; Raphaël Capart. Vortex methods and their application to trailing wake vortex simulations. Comptes Rendus. Physique, Volume 6 (2005) no. 4-5, pp. 467-486. doi : 10.1016/j.crhy.2005.05.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2005.05.001/

[1] G.-H. Cottet; P.D. Koumoutsakos Vortex Methods, Theory and Practice, Cambridge Univ. Press, Cambridge, UK, 2000

[2] G.S. Winckelmans Vortex methods (E. Stein; R. de Borst; Th.J.R. Hughes, eds.), The Encyclopedia of Computational Mechanics, vol. 3, John Wiley & Sons, October 2004

[3] P.G. Saffman Vortex Dynamics, Cambridge Univ. Press, Cambridge, UK, 1992

[4] G.S. Winckelmans; A. Leonard Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows, J. Comput. Phys., Volume 109 (1993) no. 2, pp. 247-273

[5] A. Leonard Vortex methods for flow simulation, J. Comput. Phys., Volume 37 (1980), pp. 289-335

[6] A. Leonard Computing three-dimensional incompressible flows with vortex elements, Annu. Rev. Fluid Mech., Volume 17 (1985), pp. 523-559

[7] G.S. Winckelmans, Topics in vortex methods for the computation of three- and two-dimensional incompressible unsteady flows, PhD thesis, Graduate Aeronautical Laboratories, California Institute of Technology (Advisor A. Leonard), 1989 (http://etd.caltech.edu)

[8] D. Fabre; L. Jacquin; A. Loof Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration, J. Fluid Mech., Volume 451 (2002), pp. 319-328

[9] L. Jacquin; D. Fabre; D. Sipp; V. Theofilis; H. Vollmers Instability and unsteadiness of aircraft wake vortices, Aerosp. Sci. Tech., Volume 7 (2003), pp. 577-593

[10] J.M. Ortega; R.L. Bristol; Ó. Savas Experimental study of the instability of unequal-strength counter-rotating vortex pairs, J. Fluid Mech., Volume 474 (2003), pp. 35-84

[11] P. Degond; S. Mas-Gallic The weighted particle method for convection–diffusion equations, Math. Comput., Volume 53 (1989), pp. 485-526

[12] J.-P. Choquin; S. Huberson Particle simulation of viscous flow, Comput. Fluids, Volume 17 (1989) no. 2, pp. 397-410

[13] G.-H. Cottet; S. Mas-Gallic A particle method to solve the Navier–Stokes system, Numer. Math., Volume 57 (1990), pp. 805-827

[14] G.-H. Cottet Artificial viscosity models for vortex and particle methods, J. Comput. Phys., Volume 127 (1996), pp. 299-308

[15] A.C. de Bruin, F.L.A. Ganzevles, Data analysis of wake survey tests behind SWIM model in DNW-LST and DNW-LLF windtunnels, C-Wake project, NLR-TR-2001-201, 2001

[16] P.R. Owen The decay of a turbulent trailing vortex, Aeronaut. Q., Volume 21 (1970), pp. 69-78

[17] M.I. Yaras, Numerical simulations of aircraft wake-vortex dynamics in non-uniform windshear and ground proximity, AIAA paper 2002-0940, 2002

[18] P. Ploumhans; G.S. Winckelmans Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry, J. Comput. Phys., Volume 165 (2000), pp. 354-406

[19] J.E. Barnes; P. Hut A hierarchical O(NlogN) force-calculation algorithm, Nature, Volume 324 (1986), pp. 446-449

[20] L. Greengard; V. Rohklin A fast algorithm for particle simulations, J. Comput. Phys., Volume 73 (1987), pp. 325-348

[21] J.K. Salmon; M. Warren Skeletons from the treecode closet, J. Comput. Phys., Volume 111 (1994), pp. 136-155

[22] J.K. Salmon; M. Warren; G. Winckelmans Fast parallel tree codes for gravitational and fluid dynamical N-body problems, Internat. J. Supercomput. Appl. High Performance Comput., Volume 8 (1994) no. 2, pp. 129-142

[23] J.P. Christiansen Numerical solution of hydrodynamics by the method of point vortices, J. Comput. Phys., Volume 13 (1973), pp. 363-379

[24] G.-H. Cottet; B. Michaux; S. Ossia; G. Vanderlinden A comparison of spectral and vortex methods in three-dimensional incompressible flows, J. Comput. Phys., Volume 175 (2002), pp. 702-712

[25] G.-H. Cottet; P. Poncet Particle methods for Direct Numerical Simulations of three-dimensional wakes, J. Turbulence, Volume 3 (2003) no. 028, pp. 1-9 http://jot.iop.org/

[26] P. Koumoutsakos; A. Leonard; F. Pépin Boundary conditions for viscous vortex methods, J. Comput. Phys., Volume 113 (1994), pp. 52-56

[27] P. Koumoutsakos; A. Leonard High resolution simulations of the flow around an impulsively started cylinder using vortex methods, J. Fluid Mech., Volume 296 (1995), pp. 1-38

[28] P. Koumoutsakos; D. Shiels Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate, J. Fluid Mech., Volume 328 (1996), pp. 177-226

[29] P. Ploumhans; G.S. Winckelmans; J.K. Salmon; A. Leonard; M.S. Warren Vortex methods for direct numerical simulation of three-dimensional bluff body flows: Application to the sphere at Re=300, 500 and 1000, J. Comput. Phys., Volume 178 (2002), pp. 427-463

[30] G.-H. Cottet; P. Poncet Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods, J. Comput. Phys., Volume 193 (2004), pp. 136-158

[31] P. Poncet Vanishing of mode B in the wake behind a rotating circular cylinder, Phys. Fluids, Volume 14 (2002) no. 6, p. 2021

[32] G.-H. Cottet; P.D. Koumoutsakos; M.L. Ould-Sahili Vortex methods with spatially varying cores, J. Comput. Phys., Volume 162 (2000), pp. 164-185

[33] G. Daeninck; P. Ploumhans; G.S. Winckelmans Simulation of three-dimensional bluff-body flows using vortex methods: from direct numerical simulation towards large-eddy simulation modelling, J. Turbulence, Volume 3 (2003) no. 043 http://jot.iop.org/

[34] M.L. Ould-Salihi; G.-H. Cottet; M. El Hamraoui Blending finite-difference and vortex methods for incompressible flow computations, SIAM J. Sci. Comput., Volume 22 (2000) no. 5, pp. 1655-1674

[35] P.A. Raviart An analysis of particle methods, Numerical Methods in Fluid Dynamics, Lecture Notes in Math. Ser., vol. 1127, Springer-Verlag, Berlin/New York, 1983, pp. 243-324

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Unsteadiness, instability and turbulence in trailing vortices

Laurent Jacquin; David Fabre; Denis Sipp; ...

C. R. Phys (2005)

Physics of vortex merging

Patrice Meunier; Stéphane Le Dizès; Thomas Leweke

C. R. Phys (2005)

Various aspects of fluid vortices

Ivan Delbende; Thomas Gomez; Christophe Josserand; ...

C. R. Méca (2004)