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

Volumn 19, Issue 2, 2007, Pages

  Latin, Marco ^a   Schilling, Oleg ^b   Don, Wai Sun ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^c BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DENSITY (SPECIFIC GRAVITY); PERTURBATION TECHNIQUES; SHOCK WAVES;

AMPLITUDE GROWTH MODEL; LINEAR INSTABILITY THEORY; RICHTMYER-MESHKOV INSTABILITY;

FLUID MECHANICS;

COMPUTER SIMULATION; DENSITY (SPECIFIC GRAVITY); FLUID MECHANICS; PERTURBATION TECHNIQUES; SHOCK WAVES;

EID: 33847678058     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2472508     Document Type: Article

References (71)

1. R. D. Richtmyer, "Taylor instability in shock acceleration of compressible fluids," Commun. Pure Appl. Math. 8, 297 (1960).
2. E. E. Meshkov, "Instability of the interface of two gases accelerated by a shock wave," Fluid Dyn. 4, 101 (1969).
3. N. J. Zabusky, "Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments," Annu. Rev. Fluid Mech. 31, 495 (1999).
4. M. Brouillette, "The Richtmyer-Meshkov instability," Annu. Rev. Fluid Mech. 34, 445 (2002).
5. J. D. Lindl, "Development of the indirect-drive approach to inertial con-finement fusion and the target physics basis for ignition and gain," Phys. Plasmas 2, 3933 (1995).
6. S. Nakai and H. Takabe, "Principles of inertial confinement fusion - Physics of implosion and the concept of inertial fusion energy," Rep. Prog. Phys. 59, 1071 (1996).
7. J. D. Lindl, Inertial Confinement Fusion: The Quest for Ignition and Energy Gain Using Indirect Drive (AIP, New York, 1998).
8. S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial Confinement Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter, Vol. 125 of International Series of Monographs on Physics (Oxford University Press, New York, 2004).
9. G. J. Hendricks, "Two mechanisms of vorticity generation in combusting flow fields," Ph.D. thesis, California Institute of Technology (1986).
10. S. W. Falk and W. D. Arnett, "A theoretical model for type II supernovae," Astrophys. J., Lett. 180, L65 (1973).
11. W. D. Arnett, "Supernova theory and supernova 1987A," Astrophys. J. 319, 136 (1987).
12. W. D. Arnett, B. A. Fryxell, and E. Müller, "Instabilities and nonradial motion in SN-1987A," Astrophys. J. Lett. 341, L63 (1989).
13. J. Kane, R. P. Drake, and B. A. Remington, "An evaluation of the Richtmyer-Meshkov instability in supernova remnant formation," Astrophys. J. 511, 335 (1999).
14. D. Arnett, "The role of mixing in astrophysics," Astrophys. J., Suppl. Ser. 127, 213 (2000).
15. B. D. Collins and J. W. Jacobs, "PLIF flow visualization and measurements of the Richtmyer-Meshkov instability of an air/SF6 interface," J. Fluid Mech. 464, 113 (2002).
16. G. Peng, N. J. Zabusky, and S. Zhang, "Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer-Meshkov interface," Phys. Fluids 15, 3730 (2003).
17. P. E. Dimotakis, "The mixing transition in turbulent flows," J. Fluid Mech. 409, 69 (2000).
18. K. O. Mikaelian, "Numerical simulations of Richtmyer-Meshkov instabilities in finite-thickness fluid layers," Phys. Fluids 8, 1269 (1996).
19. O. Sadot, L. Erez, G. Oron, G. Ben-Dor, U. Alon, L. A. Levin, and D. Shvarts, "Studies on the nonlinear evolution of the Richtmyer-Meshkov instability," Astrophys. J., Suppl. Ser. 127, 469 (2000).
20. J. W. Jacobs, M. A. Jones, and C. E. Niederhaus, "Experimental studies of Richtmyer-Meshkov instability," in Proceedings of the Fifth International Workshop on Compressible Turbulent Mixing, edited by R. Young, J. Glimm, and B. Boston (World Scientific, New York, 1996), pp. 195-202.
21. C. E. Niederhaus and J. W. Jacobs, "Experimental study of the Richtmyer-Meshkov instability of incompressible fluids," J. Fluid Mech. 485, 243 (2003).
22. A. D. Kotelnikov and N. J. Zabusky, "Vortex dynamics of a twiceaccelerated interface in an incompressible ideal fluid," Astrophys. J., Suppl. Ser. 127, 389 (2000).
23. A. D. Kotelnikov, J. Ray, and N. J. Zabusky, "Vortex morphologies on reaccelerated interfaces: Visualization, quantification and modeling of one- and two-mode compressible and incompressible environments," Phys. Fluids 12, 3245 (2000).
24. J. W. Jacobs, D. G. Jenkins, D. L. Klein, and R. F. Benjamin, "Nonlinear growth of the shock-accelerated instability of a thin fluid layer," J. Fluid Mech. 295, 23 (1995).
25. P. M. Rightley, P. Vorobieff, and R. F. Benjamin, "Evolution of a shockaccelerated thin fluid layer," Phys. Fluids 9, 1770 (1997).
26. K. Kremeyer, S. Nazarenko, and A. C. Newell, "Shock bowing and vorticity dynamics during propagation into different transverse density pro-files," Physica D 163, 150 (2002).
27. S. Zhang, N. J. Zabusky, G. Peng, and S. Gupta, "Shock gaseous cylinder interactions: Dynamically validated initial conditions provide excellent agreement between experiments and numerical simulations to late - intermediate time," Phys. Fluids 16, 1203 (2004).
28. C. B. Laney, Computational Gas Dynamics (Cambridge University Press, New York, 1998).
29. R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Vol. 31 of Cambridge Texts in Applied Mathematics (Cambridge University Press, New York, 2002).
30. A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, Vol. 4 of Texts in Applied Mathematics, 3rd ed. (Springer-Verlag, New York, 1993).
31. J. P. Boris, F. F. Grinstein, E. S. Oran, and R. L. Kolbe, "New insights into large eddy simulation," Fluid Dyn. Res. 10, 199 (1992).
32. D. Drikakis, "Advances in turbulent flow computations using highresolution methods," Prog. Aerosp. Sci. 39, 405 (2003).
33. M. Latini, O. Schilling, and W. S. Don, "Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability," J. Comput. Phys. 221, 805 (2007).
34. D. Balsara and C.-W. Shu, "Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy," J. Comput. Phys. 160, 405 (2000).
35. C.-W. Shu, "High order ENO and WENO schemes for computational fluid dynamics," in High-Order Methods for Computational Physics, edited by T. J. Barth and H. Deconinck (Springer-Verlag, New York, 1999), pp. 439-582.
36. S. Karni, "Multicomponent flow calculations by a consistent primitive algorithm," J. Comput. Phys. 112, 31 (1994).
37. S. Karni, "Hybrid multifluid algorithms," SIAM J. Sci. Comput. 17, 1019 (1996).
38. R. Abgrall, "How to prevent pressure oscillations in multicomponent flow calculations: A quasi-conservative approach," J. Comput. Phys. 125, 150 (1996).
39. R. Abgrall and S. Karni, "Computations of compressible multifluids," J. Comput. Phys. 169, 594 (2001).
40. C.-W. Shu and S. Osher, "Efficient implementation of essentially nonoscillatory shock-capturing schemes," J. Comput. Phys. 77, 439 (1988).
41. M. A. Jones and J. W. Jacobs, "A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface," Phys. Fluids 9, 3078 (1997).
42. J. W. Jacobs and V. V. Krivets, "Experiments on the late-time development of single-mode Richtmyer-Meshkov instability," Phys. Fluids 17, 034104 (2005).
43. G. I. Taylor, "The instability of liquid surfaces when accelerated in a direction perpendicular to their planes," Proc. R. Soc. London, Ser. A 201, 192 (1950).
44. K. A. Meyer and P. J. Blewett, "Numerical investigation of the stability of a shock accelerated interface between two fluids," Phys. Fluids 15, 753 (1972).
45. G. Fraley, "Rayleigh-Taylor stability for a normal shockwave-density discontinuity,interaction" Phys. Fluids 29, 376 (1986).
46. K. O. Mikaelian, "Freeze-out and the effect of compressibility in the Richtmyer-Meshkov instability," Phys. Fluids 6, 356 (1994).
47. M. Vandenboomgaerde, C. Mügler, and S. Gauthier, "Impulsive model for the Richtmyer-Meshkov instability," Phys. Rev. E 58, 1874 (1998).
48. Q. Zhang and S. Sohn, "Non-linear theory of unstable fluid mixing driven by shock wave," Phys. Fluids 9, 1106 (1997).
49. M. Vandenboomgaerde, S. Gauthier, and C. Mügler, "Nonlinear regime of a multimode Richtmyer-Meshkov instability: A simplified perturbation theory," Phys. Fluids 14, 1111 (2002).
50. C. Matsuoka, K. Nishihara, and Y. Fukuda, "Nonlinear evolution of an interface in the Richtmyer-Meshkov instability," Phys. Rev. E 67, 036301 (2003).
51. erratum, ibid. 68, 029902 (2003).
52. O. Sadot, L. Erez, U. Alon, D. Oron, and L. A. Levin, "Study of nonlinear evolution of single-mode and two bubble interaction under Richtmyer-Meshkov instability," Phys. Rev. Lett. 80, 1654 (1998).
53. D. Layzer, "On the instability of superposed fluids in a gravitational field," Astrophys. J. 122, 1 (1955).
54. V. N. Goncharov, "Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers," Phys. Rev. Lett. 88, 134502 (2002).
55. S.-I. Sohn, "Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios," Phys. Rev. E 67, 026301 (2003).
56. S.-I. Sohn, "Density dependence of a Zufiria-type model for Rayleigh-Taylor bubble fronts," Phys. Rev. E 70, 045301 (2004).
57. J. A. Zufiria, "Bubble competition in Rayleigh-Taylor instability," Phys. Fluids 31, 440 (1988).
58. S.-I. Sohn and Q. Zhang, "Late time behavior of bubbles at unstable interfaces in two dimensions," Phys. Fluids 13, 3493 (2001).
59. K. O. Mikaelian, "Explicit expressions for the single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers," Phys. Rev. E 67, 026319 (2003).
60. H. M. Antia, Numerical Methods for Scientists and Engineers (Birkäuser, Boston, 2002).
61. A. W. Cook and P. E. Dimotakis, "Transition stages of Rayleigh-Taylor instability between miscible fluids," J. Fluid Mech. 443, 69 (2001).
62. corrigendum, ibid. 457, 410 (2002).
63. L. F. Henderson, "On the refraction of shock waves," J. Fluid Mech. 198, 365 (1989).
64. K. O. Mikaelian, "Density gradient stabilization of the Richtmyer-Meshkov instability," Phys. Fluids A 3, 2638 (1991).
65. R. E. Duff, F. H. Harlow, and C. W. Hirt, "Effects of diffusion on interface instability between gases," Phys. Fluids 5, 417 (1962).
66. K. Sinha and G. V. Candler, "Turbulent dissipation-rate equation for compressible flows," AIAA J. 41, 1017 (2003).
67. S. Pirozzoli, F. Grasso, and T. B. Gatski, "Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25," Phys. Fluids 16, 530 (2004).
68. J. A. Ekaterinaris, "Performance of high-order-accurate, low-diffusion numerical schemes for compressible flow," AIAA J. 42, 493 (2004).
69. J. A. Ekaterinaris, "High-order accurate, low numerical diffusion methods for aerodynamics," Prog. Aerosp. Sci. 41, 192 (2005).
70. T. S. Cheng and K. S. Lee, "Numerical simulations of underexpanded supersonic jet and free shear layer using WENO schemes," Int. J. Heat Fluid Flow 26, 755 (2005).
71. B. Costa, W. S. Don, D. Gottlieb, and R. Sendersky, "Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws," Commun. Comput. Phys. 1, 548 (2006).