Direct simulation Monte Carlo investigation of the Rayleigh-Taylor instability

Gallis, M. A.; Koehler, T. P.; Torczynski, J. R.; Plimpton, S. J.

doi:10.1103/PhysRevFluids.1.043403

Title: Direct simulation Monte Carlo investigation of the Rayleigh-Taylor instability

Journal Article · Wed Aug 31 00:00:00 EDT 2016 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.1.043403· OSTI ID:1339256

Gallis, M. A. ^[1]; Koehler, T. P. ^[1]; Torczynski, J. R. ^[1]; Plimpton, S. J. ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Engineering Sciences Center
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computing Research Center

In this paper, the Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. Finally, for the conditions simulated, diffusion can influence the initial instability growth significantly.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1339256

Alternate ID(s):: OSTI ID: 1313260

Report Number(s):: SAND2016-1868J; 619643; TRN: US1701676

Journal Information:: Physical Review Fluids, Vol. 1, Issue 4; ISSN 2469-990X

Publisher:: APSCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 44 works

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References (40)

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories Dimonte, Guy; Schneider, Marilyn Physics of Fluids, Vol. 12, Issue 2 https://doi.org/10.1063/1.870309	journal	February 2000
Knudsen-number dependence of two-dimensional single-mode Rayleigh-Taylor fluid instabilities Sagert, Irina; Howell, Jim; Staber, Alec Physical Review E, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevE.92.013009	journal	July 2015
Simple model for the turbulent mixing width at an ablating surface Cherfils, Catherine; Mikaelian, Karnig O. Physics of Fluids, Vol. 8, Issue 2 https://doi.org/10.1063/1.868805	journal	February 1996
An overview of Rayleigh-Taylor instability Sharp, D. H. Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3 https://doi.org/10.1016/0167-2789(84)90510-4	journal	July 1984
The mixing transition in RayleighTaylor instability Cook, Andrew W.; Cabot, William; Miller, Paul L. Journal of Fluid Mechanics, Vol. 511 https://doi.org/10.1017/S0022112004009681	journal	January 1999
Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability Dalziel, S. B.; Linden, P. F.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 399 https://doi.org/10.1017/S002211209900614X	journal	November 1999
Fuel gain exceeding unity in an inertially confined fusion implosion Hurricane, O. A.; Callahan, D. A.; Casey, D. T. Nature, Vol. 506, Issue 7488 https://doi.org/10.1038/nature13008	journal	February 2014
Ion-kinetic simulations of D- ³ He gas-filled inertial confinement fusion target implosions with moderate to large Knudsen number Larroche, O.; Rinderknecht, H. G.; Rosenberg, M. J. Physics of Plasmas, Vol. 23, Issue 1 https://doi.org/10.1063/1.4939025	journal	January 2016
Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow Gallis, M. A.; Torczynski, J. R.; Rader, D. J. Physics of Fluids, Vol. 18, Issue 1 https://doi.org/10.1063/1.2166449	journal	January 2006
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers Goncharov, V. N. Physical Review Letters, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevLett.88.134502	journal	March 2002
Supernova 1987A Arnett, W. David; Bahcall, John N.; Kirshner, Robert P. Annual Review of Astronomy and Astrophysics, Vol. 27, Issue 1 https://doi.org/10.1146/annurev.aa.27.090189.003213	journal	September 1989
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II Lewis, D. J. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 202, Issue 1068, p. 81-96 https://doi.org/10.1098/rspa.1950.0086	journal	June 1950
Late-time quadratic growth in single-mode Rayleigh-Taylor instability Wei, Tie; Livescu, Daniel Physical Review E, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevE.86.046405	journal	October 2012
Molecular gas dynamics observations of Chapman-Enskog behavior and departures therefrom in nonequilibrium gases Gallis, M. A.; Torczynski, J. R.; Rader, D. J. Physical Review E, Vol. 69, Issue 4 https://doi.org/10.1103/PhysRevE.69.042201	journal	April 2004
Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids Livescu, D. Physics of Fluids, Vol. 16, Issue 1 https://doi.org/10.1063/1.1630800	journal	January 2004
Effects of Diffusion on Interface Instability between Gases Duff, R. E.; Harlow, F. H.; Hirt, C. W. Physics of Fluids, Vol. 5, Issue 4 https://doi.org/10.1063/1.1706634	journal	January 1962
Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability Gallis, M. A.; Koehler, T. P.; Torczynski, J. R. Physics of Fluids, Vol. 27, Issue 8 https://doi.org/10.1063/1.4928338	journal	August 2015
A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation Wagner, Wolfgang Journal of Statistical Physics, Vol. 66, Issue 3-4 https://doi.org/10.1007/BF01055714	journal	February 1992
Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations Ristorcelli, J. R.; Clark, T. T. Journal of Fluid Mechanics, Vol. 507 https://doi.org/10.1017/S0022112004008286	journal	May 2004
Monte Carlo Simulation of Gas Flows Bird, G. A. Annual Review of Fluid Mechanics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev.fl.10.010178.000303	journal	January 1978
Nonequilibrium gas flows. I: A detailed validation of Monte Carlo direct simulation for monatomic gases Erwin, Daniel A.; Pham‐Van‐Diep, Gerald C.; Muntz, E. Phillip Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 4 https://doi.org/10.1063/1.858075	journal	April 1991
Rarefied Gas Dynamics Muntz, E. P. Annual Review of Fluid Mechanics, Vol. 21, Issue 1 https://doi.org/10.1146/annurev.fl.21.010189.002131	journal	January 1989
The character of the equilibrium of an incompressible heavy viscous fluid of variable density Chandrasekhar, S. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51, Issue 1 https://doi.org/10.1017/S0305004100030048	journal	January 1955
Nonequilibrium fluctuations studied by a rarefied-gas simulation Garcia, Alejandro L. Physical Review A, Vol. 34, Issue 2 https://doi.org/10.1103/PhysRevA.34.1454	journal	August 1986
Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain Lindl, John Physics of Plasmas, Vol. 2, Issue 11 https://doi.org/10.1063/1.871025	journal	November 1995
Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability Kadau, K.; Germann, T. C.; Hadjiconstantinou, N. G. Proceedings of the National Academy of Sciences, Vol. 101, Issue 16 https://doi.org/10.1073/pnas.0401228101	journal	April 2004
Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae Cabot, William H.; Cook, Andrew W. Nature Physics, Vol. 2, Issue 8 https://doi.org/10.1038/nphys361	journal	July 2006
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I Taylor, Geoffrey Ingram Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196 https://doi.org/10.1098/rspa.1950.0052	journal	March 1950
Atomistic methods in fluid simulation Kadau, Kai; Barber, John L.; Germann, Timothy C. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1916 https://doi.org/10.1098/rsta.2009.0218	journal	April 2010
Direct simulation Monte Carlo convergence behavior of the hard-sphere-gas thermal conductivity for Fourier heat flow Rader, D. J.; Gallis, M. A.; Torczynski, J. R. Physics of Fluids, Vol. 18, Issue 7 https://doi.org/10.1063/1.2213640	journal	July 2006
Theory of the Rayleigh-Taylor instability Kull, H. J. Physics Reports, Vol. 206, Issue 5 https://doi.org/10.1016/0370-1573(91)90153-D	journal	August 1991
Transition stages of Rayleigh–Taylor instability between miscible fluids Cook, Andrew W.; Dimotakis, Paul E. Journal of Fluid Mechanics, Vol. 443 https://doi.org/10.1017/S0022112001005377	journal	September 2001
Numerical simulation of turbulent mixing by Rayleigh-Taylor instability Youngs, David L. Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3 https://doi.org/10.1016/0167-2789(84)90512-8	journal	July 1984
Investigation of the ellipsoidal-statistical Bhatnagar–Gross–Krook kinetic model applied to gas-phase transport of heat and tangential momentum between parallel walls Gallis, M. A.; Torczynski, J. R. Physics of Fluids, Vol. 23, Issue 3 https://doi.org/10.1063/1.3558869	journal	March 2011
Scaling of atomistic fluid dynamics simulations Kadau, Kai; Barber, John L.; Germann, Timothy C. Physical Review E, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevE.78.045301	journal	October 2008
Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density Proceedings of the London Mathematical Society, Vol. s1-14, Issue 1 https://doi.org/10.1112/plms/s1-14.1.170	journal	November 1882
On the Instability of Superposed Fluids in a Gravitational Field. Layzer, David The Astrophysical Journal, Vol. 122 https://doi.org/10.1086/146048	journal	July 1955
Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing Abarzhi, Snezhana I. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1916 https://doi.org/10.1098/rsta.2010.0020	journal	April 2010
Rayleigh–Taylor turbulent mixing of immiscible, miscible and stratified fluids Abarzhi, S. I.; Gorobets, A.; Sreenivasan, K. R. Physics of Fluids, Vol. 17, Issue 8 https://doi.org/10.1063/1.2009027	journal	August 2005
Atomistic simulation of the Rayleigh-Taylor instability Barber, J. L.; Kadau, K.; Germann, T. C. Journal of Physics: Conference Series, Vol. 46 https://doi.org/10.1088/1742-6596/46/1/008	journal	September 2006

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Molecular-dynamics simulation of Richtmyer-Meshkov instability on a Li-H ₂ interface at extreme compressing conditions Huang, Shenghong; Wang, Weirong; Luo, Xisheng Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5018845	journal	June 2018
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