Geodesic
Direct simulation of interacting vortex pairs
Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 21-32.

Voir la notice de l'article provenant de la source Math-Net.Ru

The coupled problem of dynamics and acoustics of two interacting vortex pairs is studied numerically for a range of Reynolds numbers, Re=5000–10000. The computations are performed on a Eulerian grid with the CABARET method. Two main integral characteristics of the vortex system, such as the period of vortex sleep through and the velocity of their centre of mass, as obtained from the computational solution, are compared with the analytical potential theory solution available for point vortices. Numerical grid sensitivity study is performed both for the hydrodynamic near-field and acoustic far-field solutions obtained.
Keywords: fluid dynamics, acoustics, high-resolution computational methods
Mots-clés : vortex interaction, CABARET scheme. 
@article{MM_2011_23_11_a2,
     author = {P. G. Yakovlev and S. A. Karabasov and V. M. Goloviznin},
     title = {Direct simulation of interacting vortex pairs},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {23},
     number = {11},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_11_a2/}
}
TY  - JOUR
AU  - P. G. Yakovlev
AU  - S. A. Karabasov
AU  - V. M. Goloviznin
TI  - Direct simulation of interacting vortex pairs
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 21
EP  - 32
VL  - 23
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_11_a2/
LA  - ru
ID  - MM_2011_23_11_a2
ER  - 
%0 Journal Article
%A P. G. Yakovlev
%A S. A. Karabasov
%A V. M. Goloviznin
%T Direct simulation of interacting vortex pairs
%J Matematičeskoe modelirovanie
%D 2011
%P 21-32
%V 23
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_11_a2/
%G ru
%F MM_2011_23_11_a2
P. G. Yakovlev; S. A. Karabasov; V. M. Goloviznin. Direct simulation of interacting vortex pairs. Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 21-32. http://geodesic.mathdoc.fr/item/MM_2011_23_11_a2/

[1] Powell A., “Theory of vortex sound”, Journal of the Acoustical Society of America, 36(1) (1964), 177–195 | DOI | MR

[2] Ffowcs Williams J. E., “Hydrodynamic Noise”, Annual Review of Fluid Mechanics, 1 (1969), 197–222 | DOI

[3] Koenig M., Cavalieri A., Jordan P., Delville J., Gervais Y., Papamoschoux D., Samimy M., Lele S., “Filtering and source imaging for the study of jet noise”, AIAA 2010-3779, 16th AIAA/CEAS Aeroacoustic Conference and Exhibit

[4] Mitchell B. E., Lele S. K., Moin P., “Direct computation of the sound from a compressible corotating vortex pair”, Journal of Fluid Mechanics, 285 (1995), 181–202 | DOI | MR | Zbl

[5] Tang S. K., Ko N. W. M., “Sound sources in the interactions of two inviscid two-dimensional vortex pairs”, Journal of Fluid Mechanics, 419 (2000), 177–201 | DOI | MR | Zbl

[6] Eldridge J. D., “The dynamics and acoustics of viscous two-dimensional leapfrogging vortices”, J. Sound Vib., 301 (2007), 74–92 | DOI

[7] Inoue O., “Sound generation by the leapfrogging between two coaxial vortex rings”, Physics of Fluids, 14:9 (2002), 3361–3364 | DOI

[8] Mohring W., “On vortex sound at low Mach number”, Journal of Fluid Mechanics, 85 (1978), 685–691 | DOI | MR

[9] Samarskii A. A., Goloviznin V. M., “Raznostnaya approksimatsiya konvektivnogo perenosa s prostranstvennym rasschepleniem vremennoi proizvodnoi”, Matem. modelirovanie, 10:1 (1998), 86–100 | MR

[10] Samarskii A. A., Goloviznin V. M., “Nekotorye svoistva raznostnoi skhemy ‘`kabare’ ”, Matem. modelirovanie, 10:1 (1998), 101–116 | MR

[11] Karabasov S. A., Goloviznin V. M., “Compact Accurately Boundary Adjusting high-Resolution Technique for Fluid Dynamics”, J. Comput. Phys., 228 (2009), 7426–7451 | DOI | MR | Zbl

[12] Tucker P. G., Karabasov S. A., “Unstructured grid solution of the eikonal equation for acoustics”, Int. J. Aeroacoustics, 8:6 (2009), 535–554 | DOI

[13] Karabasov S. A., Berloff P. S., Goloviznin V. M., “CABARET in the Ocean Gyres”, J. Ocean Model., 30 (2009), 155–168 | DOI

[14] Karabasov S. A., Goloviznin V. M., “A New Efficient High-Resolution Method for Non-Linear problems in Aeroacoustics”, AIAA Journal, 45:12 (2007), 2861–2871 | DOI

[15] Goloviznin V. M., Karabasov S. A., “Nelineinaya korrektsiya skhemy Kabare”, Matem. modelirovanie, 10:12 (1998), 107–123

[16] Goloviznin V. M., “Balansno-kharakteristicheskii metod chislennogo resheniya odnomernykh uravnenii gazovoi dinamiki v eilerovykh peremennykh”, Matem. modelirov., 18:11 (2006), 14–30 | MR | Zbl

[17] Hicks W. M., “On the mutual threading of vortex rings”, Proceedings of the Royal Society of London. Ser. A, 10 (1922), 111–131 | DOI

[18] Goloviznin V. M., Kanaev A. A., “Metod minimalnoi variatsii skhemy Kabare”, Zhurn. Vych. Matem. i Mat. Fiziki, 5 (2011)

[19] Thompson K. W., “Time dependent boundary conditions for hyperbolic systems, II”, Journal of Computational Physics, 89 (1990), 439–461 | DOI | MR | Zbl