Geodesic
Method of direct numerical simulation of turbulence with the account for the process history
Matematičeskoe modelirovanie, Tome 35 (2023) no. 7, pp. 41-62.

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

The paper offers a new approach to the direct numerical simulation of turbulent mixing of miscible and immiscible materials different in density. The idea of the approach is in separation of homogeneous mixtures the mixed cells with miscible materials from heterogeneous ones containing the fragments with contact boundaries. The article describes a 2D technique developed in EGDC (Euler Gas Dynamics with Concentrations) code to realize the approach described above. The method is verified using a classical problem of turbulent mixing as a result of Rayleigh-Taylor instability at constant acceleration of the contact boundary between two gases of different density.
Keywords: Rayleigh-Taylor instability, a turbulence mixing zone, direct numerical simulation, degree of homogeneous mixing, EGDC method. 
@article{MM_2023_35_7_a3,
     author = {Yu. V. Yanilkin and A. R. Guzhova and L. I. Degtyarenko and V. Yu. Kolobyanin and V. A. Shmelev},
     title = {Method of direct numerical simulation of turbulence with the account for the process history},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {41--62},
     publisher = {mathdoc},
     volume = {35},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_7_a3/}
}
TY  - JOUR
AU  - Yu. V. Yanilkin
AU  - A. R. Guzhova
AU  - L. I. Degtyarenko
AU  - V. Yu. Kolobyanin
AU  - V. A. Shmelev
TI  - Method of direct numerical simulation of turbulence with the account for the process history
JO  - Matematičeskoe modelirovanie
PY  - 2023
SP  - 41
EP  - 62
VL  - 35
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2023_35_7_a3/
LA  - ru
ID  - MM_2023_35_7_a3
ER  - 
%0 Journal Article
%A Yu. V. Yanilkin
%A A. R. Guzhova
%A L. I. Degtyarenko
%A V. Yu. Kolobyanin
%A V. A. Shmelev
%T Method of direct numerical simulation of turbulence with the account for the process history
%J Matematičeskoe modelirovanie
%D 2023
%P 41-62
%V 35
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2023_35_7_a3/
%G ru
%F MM_2023_35_7_a3
Yu. V. Yanilkin; A. R. Guzhova; L. I. Degtyarenko; V. Yu. Kolobyanin; V. A. Shmelev. Method of direct numerical simulation of turbulence with the account for the process history. Matematičeskoe modelirovanie, Tome 35 (2023) no. 7, pp. 41-62. http://geodesic.mathdoc.fr/item/MM_2023_35_7_a3/

[1] S. M. Bakhrakh, Yu. P. Glagoleva, M. S. Samigulin, V. D. Frolov, N. N. Yanenko, Yu. V. Yanilkin, “Rachet gazodinamicheskikh techenii na osnove metoda kontsentratsii”, DAN SSSR, 276:4 (1981), 566–569 | Zbl

[2] C. W. Hirt, B. D. Nichols, “Volume of fluid (VOF) method for dynamics of free boundaries”, J. Comp. Physics, 39:1 (1981), 201–225 | DOI | Zbl

[3] V. Dyadechko, M. Shashkov, “Reconstruction of multi-material interfaces from moment data”, J. Comp. Physics, 227:11 (2008), 5361–5384 | DOI | MR | Zbl

[4] S. I. Skrypnik, N. M. Rud'ko, R. A. Korolev, V. V. Lyapin, A. V. Popov, “Chislennoe reshenie dvumernykh uravnenii gazodinamiki s teploprovodnostiu s ispolzovaniem peremennogo po razmeru raznostnogo shablona”, VANT, ser. MMFP, 2007, no. 1, 14–26

[5] Yu. V. Yanilkin, S. P. Belyaev, Ya. A. Bondarenko i dr., “Eilerovy chislennye metodiki EGAK i TREK dlia modelirovaniia mnogomernykh techenii mnogokompomponentnoi sredy”, Trudy RFYaTs-VNIIEF. Nauch. issl. izd., 12, RFYaTs-VNIIEF, Sarov, 2008, 54–65

[6] Yu. V. Yanilkin, V. P. Statsenko, V. I. Kozlov, Matematicheskoe modelirovanie turbulentnogo peremeshivaniia szhimaemykh sredakh, Kurs lektsiy 2-kh tt., VNIIEF, Sarov, 2020

[7] V. P. Statsenko, Yu. V. Yanilkin, O. G. Sin'kova, A. L. Stadnik, “Stepen gomogennogo smesheniia po rezultatam 3D chislennykh raschetov gravitatsionnogo turbulentnogo peremeshivaniia”, VANT, ser. TPF, 2007, no. 2–3, 32–40

[8] P. F. Linden, J. M. Redondo, “Molecular mixing in Rayleigh-Taylor instability”, J. Fluid Mech. A, 3:5 (1991), 1269–1277 | MR

[9] Yu. V. Yanilkin, A. R. Guzhova, L. I. Degtyarenko, O. G. Sin'kova, “Opredelenie lokalnoi stepeni gomogennogo smesheniia pri priamom chislennom modelirovanii turbulentnogo peremeshivaniia”, VANT, ser. MMFP, 3 (2020), 3–11

[10] A. S. Kozlovskih, D. V. Neuvazhayev, “Coefficient of heterogeneity in turbulent mixing zone”, Lazer and Particle beams, 18 (2000), 207–212 | DOI

[11] Yu. V. Yanilkin, “Modeli zamykaniia uravnenii lagranzhevoi gazodinamiki i uprugoplastiki v mnogokomponentnykh iacheikakh. Ch. 1. Izotropnye modeli”, VANT, ser. MMFP, 3 (2017), 3–21

[12] Yu. V. Yanilkin, O. O. Toporova, V. Yu. Kolobyanin, “Modeli zamykaniia uravnenii lagranzhevoy gazodinamiki i uprugoplastiki v mnogokomponentnykh iacheikakh. Chast 2. Anizotropnye modeli”, VANT, ser. MMFP, 3 (2017), 22–38

[13] G. Dimonte, D. L. Youngs, A. Dimits et al., “A comparative study of the turbulent Rayleigh-Teylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration”, Phys. Fluids, 16:5 (2004), 1668–1693 | DOI | MR

[14] Yu. A. Kucherenko, A. P. Pylayev, V. D. Murzakov i dr., “Eksperimental'noe opredelenie doli molekulyarnogo peremeshivaniya na stadii razvitiya Reley-Teylorovskoy neustoychivosti metodikoy khimicheskogo indikatora”, VII Zababakhinskie nauch. chteniya (Snezhinsk, 2005)

[15] S. W. Weber, G. Dimonte, M. M. Marinak, “ALE simulations turbulent Rayleigh-Taylor instability in 2D and 3D”, 8th International Workshop on the Physics of compressible turbulent mixing (USA, Pasadena, 2001)

[16] A. W. Cook, W. Cabot, P. L. Miller, “The mixing transition in Rayleigh-Taylor instability”, J. Fluid Mech., 511 (2004), 333–362 | DOI | MR | Zbl

[17] D. L. Youngs, “Numerical simulation of mixing by Raylegh-Teylor and Richymyer-Meshkov instabilities”, Laser and Particle Beams, 12:4 (1994), 725–750 | DOI

[18] J. P. Mellado, S. Sarkar, “Large-eddy simulation of Rayleigh-Taylor turbulence with compressible miscible fluids”, Phys. Fluids, 17 (2005), 076101, 20 pp. | DOI | Zbl

[19] Yu. V. Yanilkin, V. P. Statsenko, S. V. Rebrov et al., “Study of gravitational turbulent mixing at large density differences using direct 3D numerical simulation”, 8th International Workshop on the Physics of compressible turbulent mixing (USA, Pasadena, 2001)

[20] A. L. Stadnik, V. P. Statsenko, Yu. V. Yanilkin, “Direct 3D Numerical simulation of gravitational turbulent mixing with Regard to molecular viscosity”, 9th International Workshop on Physics of Compressible Turbulent Mixing (England, Cambridge, 2004) | MR