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Published February 1, 2007 | public
Journal Article Open

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions


The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically.

Additional Information

©2007 American Institute of Physics. (Received 30 November 2006; accepted 14 December 2006; published online 27 February 2007) The authors thank Dr. Jeffrey W. Jacobs for clarifying aspects of the experiment considered in this work, Dr. Vitaliy V. Krivets for providing details not originally presented in the description of the experiments, and Dr. Karnig O. Mikaelian for useful comments on the perturbation amplitude models. M.L. acknowledges support from the Air Force Office of Scientific Research through the National Defense Science and Engineering Graduate Fellowship and the Caltech Accelerated Strategic Computing (ASC) Center. W.S.D. acknowledges support of this work by the DOE under Contract No. DE-FG02-98ER25346 and the AFOSR under Contract No. FA9550-05-1-0123. This work was also performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.


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