Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity-streamfunction and shock-capturing simulations

Latini, Marco; Schilling, Oleg; Meiron, Daniel I.

doi:10.1063/5.0179157

Title: Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity-streamfunction and shock-capturing simulations

Journal Article · 12 February 2024 · Physics of Fluids

DOI: https://doi.org/10.1063/5.0179157 · OSTI ID:2329380

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California Institute of Technology (CalTech), Pasadena, CA (United States); Northrop Grumman Aeronautics Systems, Palmdale, CA (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

In this study, two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

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

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2329380

Report Number(s):: LLNL--JRNL-856945; 1085811

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 2 Vol. 36; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (79)

Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities Mikaelian, Karnig O. Physical Review Letters, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevLett.80.508	journal	January 1998
Microscopic Richtmyer–Meshkov instability under strong shock Sun, Pengyue; Ding, Juchun; Huang, Shenghong Physics of Fluids, Vol. 32, Issue 2 https://doi.org/10.1063/1.5143327	journal	February 2020
Compressible Turbulent Mixing Young, R.; Glimm, J.; Boston, B. Proceedings of the Fifth International Workshop https://doi.org/10.1142/3328	conference	October 1996
A comparison of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability growth Latini, Marco; Schilling, Oleg Physica D: Nonlinear Phenomena, Vol. 401 https://doi.org/10.1016/j.physd.2019.132201	journal	January 2020
High-amplitude effect on single-mode Richtmyer–Meshkov instability of a light–heavy interface Wang, Hui; Wang, He; Zhai, Zhigang Physics of Fluids, Vol. 35, Issue 1 https://doi.org/10.1063/5.0132145	journal	January 2023
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
Freeze‐out and the effect of compressibility in the Richtmyer–Meshkov instability Mikaelian, Karnig O. Physics of Fluids, Vol. 6, Issue 1 https://doi.org/10.1063/1.868091	journal	January 1994
Comparison of two- and three-dimensional simulations of miscible Rayleigh-Taylor instability Cabot, W. Physics of Fluids, Vol. 18, Issue 4 https://doi.org/10.1063/1.2191856	journal	April 2006
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing Zhang, Qiang Physical Review Letters, Vol. 81, Issue 16 https://doi.org/10.1103/PhysRevLett.81.3391	journal	October 1998
High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data Schilling, Oleg; Latini, Marco Acta Mathematica Scientia, Vol. 30, Issue 2 https://doi.org/10.1016/S0252-9602(10)60064-1	journal	March 2010
Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows Johnsen, Eric; Ham, Frank Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.04.048	journal	July 2012
2D single-mode Richtmyer–Meshkov instability Probyn, M. G.; Williams, R. J. R.; Thornber, B. Physica D: Nonlinear Phenomena, Vol. 418 https://doi.org/10.1016/j.physd.2020.132827	journal	April 2021
Transition stages of Rayleigh–Taylor instability between miscible fluids Cook, A. W.; Dimotakis, P. E. Journal of Fluid Mechanics, Vol. 457 https://doi.org/10.1017/S0022112002007802	journal	April 2002
Computations of Compressible Multifluids Abgrall, Rémi; Karni, Smadar Journal of Computational Physics, Vol. 169, Issue 2 https://doi.org/10.1006/jcph.2000.6685	journal	May 2001
Assessment of Very High Order of Accuracy in Implicit LES models Mosedale, Andrew; Drikakis, Dimitris Journal of Fluids Engineering, Vol. 129, Issue 12 https://doi.org/10.1115/1.2801374	journal	July 2007
Linear and nonlinear interactions between an interface and bulk vortices in Richtmyer–Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu; Cobos-Campos, Francisco Physics of Plasmas, Vol. 27, Issue 11 https://doi.org/10.1063/5.0016553	journal	November 2020
Universal perturbation growth of Richtmyer–Meshkov instability for minimum-surface featured interface induced by weak shock waves Liang, Yu; Liu, Lili; Zhai, Zhigang Physics of Fluids, Vol. 33, Issue 3 https://doi.org/10.1063/5.0045122	journal	March 2021
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I Zhou, Ye Physics Reports, Vol. 720-722 https://doi.org/10.1016/j.physrep.2017.07.005	journal	December 2017
Growth rate of the Richtmyer-Meshkov instability at shocked interfaces Mikaelian, Karnig O. Physical Review Letters, Vol. 71, Issue 18 https://doi.org/10.1103/PhysRevLett.71.2903	journal	November 1993
Vortex paradigm for shock-accelerated density-stratified interfaces Hawley, John F.; Zabusky, Norman J. Physical Review Letters, Vol. 63, Issue 12 https://doi.org/10.1103/PhysRevLett.63.1241	journal	September 1989
A membraneless experiment for the study of Richtmyer–Meshkov instability of a shock-accelerated gas interface Jones, M. A.; Jacobs, J. W. Physics of Fluids, Vol. 9, Issue 10 https://doi.org/10.1063/1.869416	journal	October 1997
Computing multi-mode shock-induced compressible turbulent mixing at late times Oggian, T.; Drikakis, D.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 779 https://doi.org/10.1017/jfm.2015.392	journal	August 2015
Numerical Calculation of Three-Dimensional Interfacial Potential Flows Using the Point Vortex Method Haroldsen, David J.; Meiron, Daniel I. SIAM Journal on Scientific Computing, Vol. 20, Issue 2 https://doi.org/10.1137/S1064827596302060	journal	January 1998
Experiments on the late-time development of single-mode Richtmyer–Meshkov instability Jacobs, J. W.; Krivets, V. V. Physics of Fluids, Vol. 17, Issue 3 https://doi.org/10.1063/1.1852574	journal	March 2005
Asymptotic growth in the linear Richtmyer–Meshkov instability Wouchuk, Juan Gustavo; Nishihara, Katsunobu Physics of Plasmas, Vol. 4, Issue 4 https://doi.org/10.1063/1.872191	journal	April 1997
Vortex Dynamics of a Twice‐accelerated Interface in an Incompressible Ideal Fluid Kotelnikov, Alexei D.; Zabusky, Norman J. The Astrophysical Journal Supplement Series, Vol. 127, Issue 2 https://doi.org/10.1086/313341	journal	April 2000
Nonlinear evolution of an interface in the Richtmyer-Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu; Fukuda, Yuko Physical Review E, Vol. 67, Issue 3 https://doi.org/10.1103/PhysRevE.67.036301	journal	March 2003
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
A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel Journal of Computational Physics, Vol. 181, Issue 2 https://doi.org/10.1006/jcph.2002.7143	journal	September 2002
A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities Ramani, Raaghav; Shkoller, Steve Journal of Computational Physics, Vol. 405 https://doi.org/10.1016/j.jcp.2019.109177	journal	March 2020
Experimental study of the Richtmyer–Meshkov instability of incompressible fluids Niederhaus, C. E.; Jacobs, J. W. Journal of Fluid Mechanics, Vol. 485 https://doi.org/10.1017/S002211200300452X	journal	May 2003
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
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Erratum: Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability [Phys. Rev. E76, 026319 (2007)] Schilling, Oleg; Latini, Marco; Don, Wai Sun Physical Review E, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevE.85.049904	journal	April 2012
A comparative numerical study of the Richtmyer-Meshkov instability with nonlinear analysis in two and three dimensions Li, X. L.; Zhang, Q. Physics of Fluids, Vol. 9, Issue 10 https://doi.org/10.1063/1.869415	journal	October 1997
Amplitude growth rate of a Richtmyer–Meshkov unstable two-dimensional interface to intermediate times Zabusky, Norman J.; Kotelnikov, Alexei D.; Gulak, Yuriy Journal of Fluid Mechanics, Vol. 475 https://doi.org/10.1017/S0022112002002732	journal	January 2003
Nonlinear theory of unstable fluid mixing driven by shock wave Zhang, Qiang; Sohn, Sung-Ik Physics of Fluids, Vol. 9, Issue 4 https://doi.org/10.1063/1.869202	journal	April 1997
Late time behavior of bubbles at unstable interfaces in two dimensions Sohn, Sung-Ik; Zhang, Qiang Physics of Fluids, Vol. 13, Issue 11 https://doi.org/10.1063/1.1410119	journal	November 2001
VORTEX PARADIGM FOR ACCELERATED INHOMOGENEOUS FLOWS: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov Environments Zabusky, Norman J. Annual Review of Fluid Mechanics, Vol. 31, Issue 1 https://doi.org/10.1146/annurev.fluid.31.1.495	journal	January 1999
Influence of subgrid scales on resolvable turbulence and mixing in Rayleigh–Taylor flow Cabot, William H.; Schilling, Oleg; Zhou, Ye Physics of Fluids, Vol. 16, Issue 3 https://doi.org/10.1063/1.1636477	journal	March 2004
Universality and scaling laws among fingers at Rayleigh–Taylor and Richtmyer–Meshkov unstable interfaces in different dimensions Guo, Wenxuan; Zhang, Qiang Physica D: Nonlinear Phenomena, Vol. 403 https://doi.org/10.1016/j.physd.2019.132304	journal	February 2020
Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts Sohn, Sung-Ik Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevE.70.045301	journal	October 2004
Richtmyer--Meshkov instability with ionization at extreme impact conditions Huang, Shenghong; Zhang, Jiawei; Ding, Juchun Physics of Fluids, Vol. 34, Issue 7 https://doi.org/10.1063/5.0095991	journal	July 2022
Nonlinear interaction between bulk point vortices and an unstable interface with nonuniform velocity shear such as Richtmyer–Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu Physics of Plasmas, Vol. 27, Issue 5 https://doi.org/10.1063/1.5131701	journal	May 2020
Linear perturbation growth at a shocked interface Wouchuk, Juan Gustavo; Nishihara, Katsunobu Physics of Plasmas, Vol. 3, Issue 10 https://doi.org/10.1063/1.871940	journal	October 1996
Quantitative theory for spikes and bubbles in the Richtmyer-Meshkov instability at arbitrary density ratios Zhang, Qiang; Guo, Wenxuan Physical Review Fluids, Vol. 7, Issue 9 https://doi.org/10.1103/PhysRevFluids.7.093904	journal	September 2022
Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface Peng, Gaozhu; Zabusky, Norman J.; Zhang, Shuang Physics of Fluids, Vol. 15, Issue 12 https://doi.org/10.1063/1.1621628	journal	December 2003
Vortex core dynamics and singularity formations in incompressible Richtmyer-Meshkov instability Matsuoka, Chihiro; Nishihara, Katsunobu Physical Review E, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevE.73.026304	journal	February 2006
Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability Latini, Marco; Schilling, Oleg; Don, Wai Sun Journal of Computational Physics, Vol. 221, Issue 2 https://doi.org/10.1016/j.jcp.2006.06.051	journal	February 2007
High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions Latini, Marco; Schilling, Oleg; Don, Wai Sun Physics of Fluids, Vol. 19, Issue 2 https://doi.org/10.1063/1.2472508	journal	February 2007
Inviscid and viscous vortex models for Richtmyer–Meshkov instability Sohn, Sung-Ik Fluid Dynamics Research, Vol. 43, Issue 6 https://doi.org/10.1088/0169-5983/43/6/065506	journal	November 2011
Multicomponent Flow Calculations by a Consistent Primitive Algorithm Karni, Smadar Journal of Computational Physics, Vol. 112, Issue 1 https://doi.org/10.1006/jcph.1994.1080	journal	May 1994
Hybrid Multifluid Algorithms Karni, Smadar SIAM Journal on Scientific Computing, Vol. 17, Issue 5 https://doi.org/10.1137/S106482759528003X	journal	September 1996
Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts Hecht, Jacob; Alon, Uri; Shvarts, Dov Physics of Fluids, Vol. 6, Issue 12 https://doi.org/10.1063/1.868391	journal	December 1994
Numerical study of the Richtmyer–Meshkov instability of a three-dimensional minimum-surface featured SF6/air interface Guan, Ben; Wang, Dayi; Wang, Ge Physics of Fluids, Vol. 32, Issue 2 https://doi.org/10.1063/1.5141783	journal	February 2020
Taylor instability in shock acceleration of compressible fluids Richtmyer, Robert D. Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130207	journal	May 1960
PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF ₆ interface Collins, B. D.; Jacobs, J. W. Journal of Fluid Mechanics, Vol. 464 https://doi.org/10.1017/S0022112002008844	journal	August 2002
Three-dimensional vortex sheet motion with axial symmetry in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities Matsuoka, Chihiro Physica Scripta, Vol. T155 https://doi.org/10.1088/0031-8949/2013/T155/014013	journal	July 2013
Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability Schilling, Oleg; Latini, Marco; Don, Wai Sun Physical Review E, Vol. 76, Issue 2 https://doi.org/10.1103/PhysRevE.76.026319	journal	August 2007
Effect of adiabatic index on Richtmyer–Meshkov flows induced by strong shocks Wright, Cameron E.; Abarzhi, Snezhana I. Physics of Fluids, Vol. 33, Issue 4 https://doi.org/10.1063/5.0041032	journal	April 2021
Kinetic energy generated by the incompressible Richtmyer–Meshkov instability in a continuously stratified fluid Saffman, P. G.; Meiron, D. I. Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 11 https://doi.org/10.1063/1.857503	journal	November 1989
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II Zhou, Ye Physics Reports, Vol. 723-725 https://doi.org/10.1016/j.physrep.2017.07.008	journal	December 2017
Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory Vandenboomgaerde, Marc; Gauthier, Serge; Mügler, Claude Physics of Fluids, Vol. 14, Issue 3 https://doi.org/10.1063/1.1447914	journal	March 2002
Numerical simulation of a Richtmyer–Meshkov instability with an adaptive central-upwind sixth-order WENO scheme Tritschler, V. K.; Hu, X. Y.; Hickel, S. Physica Scripta, Vol. T155 https://doi.org/10.1088/0031-8949/2013/T155/014016	journal	July 2013
Vortex morphologies on reaccelerated interfaces: Visualization, quantification and modeling of one- and two-mode compressible and incompressible environments Kotelnikov, Alexei D.; Ray, Jaideep; Zabusky, Norman J. Physics of Fluids, Vol. 12, Issue 12 https://doi.org/10.1063/1.1321264	journal	December 2000
Quantitative theory of Richtmyer-Meshkov instability in three dimensions Zhang, Q.; Sohn, S. -I. Zeitschrift für angewandte Mathematik und Physik, Vol. 50, Issue 1 https://doi.org/10.1007/s000330050137	journal	January 1999
Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability Sadot, O.; Erez, L.; Alon, U. Physical Review Letters, Vol. 80, Issue 8 https://doi.org/10.1103/PhysRevLett.80.1654	journal	February 1998
Density gradient stabilization of the Richtmyer–Meshkov instability Mikaelian, Karnig O. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 11 https://doi.org/10.1063/1.858152	journal	November 1991
Quantitative theory for spikes and bubbles in the Richtmyer−Meshkov instability at arbitrary density ratios in three dimensions Guo, Wenxuan; Zhang, Qiang Physics of Fluids, Vol. 34, Issue 7 https://doi.org/10.1063/5.0098888	journal	July 2022
Bubble competition in Rayleigh–Taylor instability Zufiria, Juan A. Physics of Fluids, Vol. 31, Issue 3 https://doi.org/10.1063/1.866825	journal	January 1988
Richtmyer–Meshkov-like instabilities and early-time perturbation growth in laser targets and Z-pinch loads Velikovich, A. L.; Dahlburg, J. P.; Schmitt, A. J. Physics of Plasmas, Vol. 7, Issue 5 https://doi.org/10.1063/1.873986	journal	May 2000
Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy Balsara, Dinshaw S.; Shu, Chi-Wang Journal of Computational Physics, Vol. 160, Issue 2 https://doi.org/10.1006/jcph.2000.6443	journal	May 2000
T HE R ICHTMYER -M ESHKOV I NSTABILITY Brouillette, Martin Annual Review of Fluid Mechanics, Vol. 34, Issue 1 https://doi.org/10.1146/annurev.fluid.34.090101.162238	journal	January 2002
Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers Mikaelian, Karnig O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026319	journal	February 2003
Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios Sohn, Sung-Ik Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026301	journal	February 2003
How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: A Quasi Conservative Approach Abgrall, Rémi Journal of Computational Physics, Vol. 125, Issue 1 https://doi.org/10.1006/jcph.1996.0085	journal	April 1996
Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws Samtaney, Ravi; Zabusky, Norman J. Journal of Fluid Mechanics, Vol. 269 https://doi.org/10.1017/S0022112094001485	journal	June 1994
Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities Sohn, Sung-Ik Physical Review E, Vol. 69, Issue 3 https://doi.org/10.1103/PhysRevE.69.036703	journal	March 2004
Universality of finger growth in two-dimensional Rayleigh–Taylor and Richtmyer–Meshkov instabilities with all density ratios Zhang, Qiang; Guo, Wenxuan Journal of Fluid Mechanics, Vol. 786 https://doi.org/10.1017/jfm.2015.641	journal	November 2015

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