Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T11:06:31.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Arbitrary Lagrange–Eulerian code simulations of turbulent Rayleigh–Taylor instability in two and three dimensions

Published online by Cambridge University Press:  03 March 2004

S.V. WEBER ,
G. DIMONTE  and
M.M. MARINAK
S.V. WEBER
Affiliation:
Lawrence Livermore National Laboratory, Berkeley, California
G. DIMONTE
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico
M.M. MARINAK
Affiliation:
Lawrence Livermore National Laboratory, Berkeley, California
Get access Rights & Permissions [Opens in a new window]

Abstract

We have performed simulations of the evolution of the turbulent Rayleigh–Taylor instability with an arbitrary Lagrange–Eulerian code. The problem specification was defined by Dimonte et al. (2003) for the “alpha group” code intercomparison project. Perfect γ = 5/3 gases of densities 1 and 3 g/cm3 are accelerated by constant gravity. The nominal problem uses a 2562 × 512 mesh with initial random multiwavelength interface perturbations. We have also run three-dimensional problems with smaller meshes and two-dimensional (2D) problems of several mesh sizes. Under-resolution lowered linear growth rates of the seed modes to 5-60% of the analytic values, depending on wavelength and orientation to the mesh. However, the mix extent in the 2D simulations changed little with grid refinement. Simulations without interface reconstruction gave penetration only slightly reduced from the case with interface reconstruction. Energy dissipation differs little between the two cases. The slope of the penetration distance versus time squared, corresponding to the α parameter in h = αAgt2, decreases with increasing time in these simulations. The slope, α, is consistent with the linear electric motor data of Dimonte and Schneider (2000), but the growth is delayed in time.

Keywords

Arbitrary Lagrange–Eulerian codeRayleigh–Taylor instabilityTurbulent
Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 455 - 461
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Annuchina, N.N. et al. (1978). Turbulent mixing at an accelerating interface between liquids of different densities. Izv. Akad. Nauk. SSSR, Mekh Zhidk Gaza 6, 157–160.Google Scholar
Clark, T. & Harlow, F.H. (2002). Modeling radiation effects in mixing layers. Proc. 8th International Workshop on the Physics of Compressible Turbulent Mixing, (Schilling, O., Ed.). Livermore, CA: Lawrence Livermore National Laboratory.
Cook, A.W. & Dimotakis, P.E. (2001). Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 69–99.Google Scholar
Dimonte, G. & Schneider, M. (2000). Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321.Google Scholar
Dimonte, G., Youngs, D.L., Dimits, A., Weber, S., Marinak, M., Wunsch, S., Garasi, C., Robinson, A., Andrews, M.J., Ramaprabhu, P., Calderl, A.C., Fryxell, B., Biello, J., Dursil, L., MacNeice, P., Olson, K., Ricker, P., Rosner, R., Timmes, F., Tufo, H., Young, Y.-N. & Zingale, Y.-N. (2003). A comparative study of the turbulent Rayleigh–Taylor (RT) instability using high-resolution 3D numerical simulations: The Alpha-Group collaboration. Submitted to Phys. Fluids.Google Scholar
Glimm, J., Grove, J.W., Li, X.L., Oh, W & Sharp, D.H. (2001). A critical analysis of Rayleigh–Taylor growth rates. J. Comp. Phys. 169, 652–677.Google Scholar
Hecht, J., Offer, D., Alon, U., Shvarts, D., Orsag, S.A. & McCrory, R.L. (1995). Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh–Taylor instability. Laser Part. Beams 13, 423–440.Google Scholar
Lindl, J. (1995). Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas 2, 3933–4024.CrossRefGoogle Scholar
Marinak, M.M., Tipton, R.E., Landen, O.L., Murphy, T.J., Amendt, P., Haan, S.W., Hatchett, S.P., Keane, C.J., McEachern, R. & Wallace, R. (1996). Three-dimensional simulations of Nova high growth factor capsule implosion experiments. Phys. Plasmas 3, 2070–2076.Google Scholar
Marinak, M.M., Kerbel, G.D., Gentile, N.A., Jones, O., Pollaine, S., Dittrich, T.R. & Haan, S.W. (2001). Three-dimensional HYDRA simulations of National Ignition Facility targets. Phys. Plasmas 8, 2275–2280.Google Scholar
Rayleigh, J.W.S. (1900). Scientific Papers, Vol. II, p. 200. Cambridge, UK: Cambridge University Press.
Read, K.I. (1984). Experimental investigation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 45–58.Google Scholar
Taylor, G.I. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their plane. Proc. R. Soc. London, Ser. A 201, 192–196.Google Scholar
Young, Y.-N., Tufo, H., Dubey, A. & Rosner, R. (2001). On the miscible Rayleigh–Taylor instability: Two and three dimensions. J. Fluid Mech. 447, 377–408.Google Scholar
Youngs, D.L. (1984). Numerical simulation or turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 32–44.Google Scholar
Youngs, D.L. (1994). Numerical simulation of mixing by Rayleigh–Taylor and Richmyer–Meshkov instabilities. Laser Part. Beams 12, 725–750.Google Scholar