Geodesic
Application of the CABARET algorithm for modeling turbulent mixing on the example of the Richtmyer--Meshkov instability
Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 3-16.

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

Using previously constructed by authors CABARET algorithm for multicomponent gas mixtures movement calculation, a numerical simulation of a physical instability, emerging during the passage of a shock wave through initially resting boundary between gaseous media with different physical properties, followed by turbulization of the flow in flat geometry. Simulation of two problems is carried out: the passage of a shock wave through a rectangular subdomain filled with heavy gas and the development of Richtmyer–Meshkov instability during the passage of a shock wave through the sinusoidal interface between the media. A comparison of the evolution of the mixing zone width with the experimental, theoretical and numerical results of other authors is conducted.
Mots-clés : CABARET scheme
Keywords: turbulent mixing, Richtmyer–Meshkov instability. 
@article{MM_2018_30_8_a0,
     author = {A. V. Danilin and A. V. Solovjev},
     title = {Application of the {CABARET} algorithm for modeling turbulent mixing on the example of the {Richtmyer--Meshkov} instability},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {30},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_8_a0/}
}
TY  - JOUR
AU  - A. V. Danilin
AU  - A. V. Solovjev
TI  - Application of the CABARET algorithm for modeling turbulent mixing on the example of the Richtmyer--Meshkov instability
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 3
EP  - 16
VL  - 30
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_8_a0/
LA  - ru
ID  - MM_2018_30_8_a0
ER  - 
%0 Journal Article
%A A. V. Danilin
%A A. V. Solovjev
%T Application of the CABARET algorithm for modeling turbulent mixing on the example of the Richtmyer--Meshkov instability
%J Matematičeskoe modelirovanie
%D 2018
%P 3-16
%V 30
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_8_a0/
%G ru
%F MM_2018_30_8_a0
A. V. Danilin; A. V. Solovjev. Application of the CABARET algorithm for modeling turbulent mixing on the example of the Richtmyer--Meshkov instability. Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 3-16. http://geodesic.mathdoc.fr/item/MM_2018_30_8_a0/

[1] R.D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids”, Communications on Pure and Applied Mathematics, 13 (1960), 297–319 | DOI | MR

[2] E.E. Meshkov, “Instability of the Interface of Two Gases Accelerated by a Shock Wave”, Soviet Fluid Dynamics, 1969, no. 4, 101–104

[3] K.A. Meyer, P.J. Blewett, “Numerical Investigation of Stability of a Shock-Accelerated Interface between Two Fluids”, Physics of Fluids, 15:3 (1972), 753–759 | DOI

[4] Q. Zhang, S.I. Sohn, “Nonlinear Theory of Unstable Fluid Mixing Driven by Shock Wave”, Physics of Fluids, 9:4 (1997), 1106–1124 | DOI | MR | Zbl

[5] O. Sadot, L. Erez, U. Alon, D. Oren, L.A. Levin, “Study of Nonlinear Evolution of Singlemode and Two-bubble Interaction under Richtmyer-Meshkov Instability”, Physical Review Letters, 80:8 (1998), 1654–1657 | DOI

[6] G.C. Orlicz, S. Balasubramanian, K.P. Prestridge, “Incident shock Mach number effects on Richtmyer-Meshkov mixing in a heavy gas layer”, Physics of Fluids, 25 (2013), 114101 | DOI

[7] B.D. Collins, J.W. Jacobs, “PLIF Flow Visualization and Measurements of the Richtmyer–Meshkov Instability of an air/SF6 Interface”, Journal of Fluid Mechanics, 464 (2002), 113–136 | DOI | Zbl

[8] B.E. Motl, Experimental Parameter Study of the Richtmyer–Meshkov Instability, PhD Thesis, University of Wisconsin, Madison, 2008 | Zbl

[9] E. Leinov, G. Malamud et al., “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions”, Journal of Fluid Mechanics, 626 (2009), 449–475 | DOI | Zbl

[10] J.-F. Haas, B. Sturtevant, “Interaction of Weak Shock Waves with Cylindrical and Spherical Gas Inhomogeneities”, Journal of Fluid Mechanics, 181 (1987), 41–76 | DOI

[11] D.A. Holder et al., “Shock-Tube Experiments on Richtmyer–Meshkov Instability Growth Using an Enlarged Double Bump Perturbation”, Laser and Particle Beams, 21:3 (2003), 411–418

[12] R. Abgrall, “How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach”, J. of Comp. Physics, 125:1 (1996), 150–160 | DOI | MR | Zbl

[13] M. Latini, O. Schiling, W.S. Don, “High-resolution Simulations and Modeling of Reshocked Single-mode Richtmyer–Meshkov Instability: Comparison to Experimental Data and to Amplitude Growth Model Predictions”, Physics of Fluids, 19:2 (2007), 024104 | DOI | MR | Zbl

[14] M. Latini, O. Schiling, W.S. Don, “Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability”, Journal of Computational Physics, 221 (2007), 805–836 | DOI | MR | Zbl

[15] V.F. Tishkin, V.V. Nikishin, I.V. Panov, A.P. Favorskii, “Raznostnye skhemy trekhmernoi gazovoi dinamiki dlia zadach o razvitii neustoichivosti Rikhrmaera–Meshkova”, Mathematicheskoe modelirovanie, 7:5 (1995), 15–25

[16] P. Movahed, E. Johnsen, “Numerical simulations of the Richtmyer-Meshkov instability with reshock”, 20th AIAA Computational Fluid Dynamics Conference (2011, Honolulu)

[17] P. Movahed, E. Johnsen, “A solution-adaptive method for efficient compressible multifluid simulations, with application to the Richtmyer–Meshkov instability”, Journal of Computational Physics, 239 (2013), 166–186 | DOI | MR

[18] V.K. Tritschler, X.Y. Hu, S. Hickel, N.A. Adams, “Numerical simulation of a Richtmyer–Meshkov instability with an adaptive central-upwind sixth-order WENO scheme”, Physica Scripta, 155 (2013), 014016 | DOI

[19] S. Ukai, K. Balakrishnan, S. Menon, “Growth rate predictions of single- and multi-mode Richtmyer–Meshkov instability with reshock”, Shock Waves, 21 (2011), 533–546 | DOI

[20] A. Yosef-Hai, O. Sadot et al., “Late-time growth of the Richtmyer–Meshkov instability for different Atwood numbers and different dimensionalities”, Laser and Particle Beams, 21 (2003), 363–368 | DOI

[21] J.T. Moran-Lopez, Multicomponent Reynolds-Averaged Navier-Stokes Modeling of Reshocked Richtmyer-Meshkov Instability-Induced Turbulent Mixing Using the Weighted Essentially Nonoscillatory Method, PhD Thesis, Univ. of Michigan, Ann Arbor, 2013

[22] K.R. Bates, N. Nikiforakis, D. Holder, “Richtmyer–Meshkov Instability Induced by the Interaction of a Shock Wave with a Rectangular Block of SF6”, Physics o Fluids, 19 (2007), 036101 | DOI | Zbl

[23] R.S. Lagumbay, Modeling and Simulation of Multiphase/Multicomponent Flows, PhD Thesis, University of Colorado, Boulder, 2006

[24] V.M. Goloviznin, A.A. Samarskii, “Raznostnaia approksimatsiia konvektivnogo perenosa s prostranstvennym rashchepleniem vremmennoi proizvodnoi”, Matematicheskoe modelirovanie, 10:1 (1998), 86–100

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

[26] V.M. Goloviznin, S.A. Karabasov, “Nelineinaia korrektsiia skhemy Kabare”, Matematicheskoe modelirovanie, 10:12 (1998), 107–123

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

[28] V.M. Goloviznin, “Balansno-kharakteristichskii metod chislennogo resheniia odnomernykh uravnenii gazovoi dinamiki v eilerovykh peremennykh”, Matematicheskoe modelirovanie, 18:11 (2006), 14–30 | Zbl

[29] V.M. Goloviznin, V.N. Semenov, I.A. Korotkin, S.A. Karabasov, “A novel computational method for modelling stochastic advection in heterogeneous media”, Transport in Porous Media, 66:3 (2007), 439–456 | DOI | MR

[30] A.V. Danilin, A.V. Solovjev, “A Modification of the CABARET Scheme for the Computation of Multicomponent Gaseous Flows”, Numerical Methods and Programming, 16 (2015), 18–25

[31] A.V. Danilin, A.V. Solovjev, A.M. Zaitsev, “A modification of the CABARET scheme for numerical simulation of multicomponent gaseous flows in two-dimensional domains”, Numerical Methods and Programming, 16 (2015), 436–445