Geodesic
CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 898-913 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The CABARET method was generalized to two-dimensional incompressible fluids in terms of velocity and pressure. The resulting algorithm was verified by computing the transport and interaction of various vortex structures: a stationary and a moving solitary vortex, Taylor-Green vortices, and vortices formed by the instability of double shear layers. Much attention was also given to the modeling of homogeneous isotropic turbulence and to the analysis of its spectral properties. It was shown that, regardless of the mesh size, the slope of the energy spectra up to the highest-frequency harmonics is equal $-3$, which agrees with Batchelor’s enstrophy cascade theory. 
@article{ZVMMF_2013_53_6_a5,
     author = {V. Yu. Glotov and V. M. Goloviznin},
     title = {CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {898--913},
     year = {2013},
     volume = {53},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a5/}
}
TY  - JOUR
AU  - V. Yu. Glotov
AU  - V. M. Goloviznin
TI  - CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 898
EP  - 913
VL  - 53
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a5/
LA  - ru
ID  - ZVMMF_2013_53_6_a5
ER  - 
%0 Journal Article
%A V. Yu. Glotov
%A V. M. Goloviznin
%T CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 898-913
%V 53
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a5/
%G ru
%F ZVMMF_2013_53_6_a5
V. Yu. Glotov; V. M. Goloviznin. CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 898-913. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a5/

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

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

[3] Rouch P., Vychislitelnaya gidrodinamika, Mir, M., 1980, 160–161

[4] Goloviznin V. M., Karabasov S. A., Kobrinskii I. M., “Balansno-kharakteristicheskie skhemy s razdelennymi konservativnymi i potokovymi peremennymi”, Matem. modelirovanie, 15:9 (2003), 29–48 | MR | Zbl

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

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

[7] Glotov V. Yu., Goloviznin V. M., “Skhema Kabare dlya dvumernoi neszhimaemoi zhidkosti v peremennykh “funktsiya toka-zavikhrennost””, Matem. modelirovanie, 23:9 (2011), 89–104 | MR | Zbl

[8] Danilin A. V., Goloviznin V. M., “Skhema Kabare v peremennykh “zavikhrennost-skorost” dlya chislennogo modelirovaniya dvizheniya idealnoi zhidkosti v dvumernoi oblasti”, Matem. modelirovanie, 24:5 (2012), 45–60 | MR

[9] Alekseenko S. V., Kuibin P. A., Okulov V. L., Vvedenie v teoriyu kontsentrirovannykh vikhrei, Institut teplofiziki SO RAN, Novosibirsk, 2003 | MR | Zbl

[10] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[11] Zhou Y. C., Wei G. W., “High resolution conjugate filters for the simulation of flows”, J. Comput. Phys., 189 (2003), 159–179 | DOI | MR | Zbl

[12] Walsh O., “Eddy solutions of the Navier–Stockes equations”, The NSE II-Theory and Numerical Methods, Springer, 1992, 306–309 | MR

[13] Sommeria J., “Experimental study of the two-dimensional inverse energy cascade in a square box”, J. Fluid Mech., 170 (1986), 139–168 | DOI

[14] Tabeling P., Hansen A. E., Paret J., “Forced and decaying 2D turbulence: experimental study”, Lecture Notes in Physics, 511, 1998, 145–169 | DOI | MR | Zbl

[15] Chandra Das, Shigeo Kida, Susumu Goto, “Overall self-similar decay of two-dimensional turbulence”, J. Phys. Society of Japan, 70:4 (2001), 966–976 | DOI | Zbl

[16] Frik P. G., Turbulentnost: podkhody i modeli, Institut kompyuternykh issledovanii, M.–Izhevsk, 2003

[17] Love M. D., “Subgrid modeling studies with Burgers' equation”, J. Fluid Mech., 100, Part 1 (1980), 87–110 | DOI | MR | Zbl

[18] Tabeling P., “Two-dimensional turbulence: a physicist approach”, Physics Reports, 362 (2002), 1–62 | DOI | MR | Zbl

[19] Paret J., Tabeling P., “Experimental observation of the two-dimensional inverse energy cascade”, Phys. Rev. Lett., 79 (1997), 4162–4165 | DOI

[20] Saffman P. G., “On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number”, Stud. App. Math., 1971, no. 50, 377–383 | Zbl

[21] Bengt Fornberng, “A Numerical Study of 2D-Turbulence”, J. Comput. Phys., 25:1 (1977) (Reprinted) | Zbl

[22] Kevlahan N. K.-R., Farge M., “Vorticity filaments in two-dimensional turbulence: creation, stability and effect”, J. Fluid Mech., 346 (1997), 49–76 | DOI | MR | Zbl

[23] Volkov K. N., Emelyanov V. N., Modelirovanie krupnykh vikhrei v raschetakh turbulentnykh techenii, Fizmatlit, M., 2008

[24] Karabasov S. A., Goloviznin V. M., “New efficient high-resolution method for nonlinear problems in aeroacoustic”, AIAA J., 45:12 (2007), 2861–2871 | DOI