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Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities


In this work, we investigate the growth of interface perturbations following the interaction of a shock wave with successive layers of fluids. Using the Discontinuous Galerkin method, we solve the two-dimensional multifluid Euler equations. In our setup, a shock impacts up to four adjacent fluids with perturbed interfaces. At each interface, the incoming shock generates reflected and transmitted shocks and rarefactions, which further interact with the interfaces. By monitoring perturbation growth, we characterize the influence these instabilities have on each other and the fluid mixing as a function of time in different configurations. If the third gas is lighter than the second, the reflected rarefaction at the second interface amplifies the growth at the first interface. If the third gas is heavier, the reflected shock decreases the growth and tends to reverse the Richtmyer–Meshkov instability as the thickness of the second gas is increased. We further investigate the effect of the reflected waves on the dynamics of the small scales and show how a phase difference between the perturbations or an additional fluid layer can enhance growth. This study supports the idea that shocks and rarefactions can be used to control the instability growth.

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    Since the present simulations are two-dimensional, they cannot represent vortex stretching, and thus turbulence. By TKE, our intent is to describe the energy contained in the small scales.


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This research was supported in part by the DOE NNSA/ASC under the predictive Science Academic Alliance Program by Grant No. DEFC52-08NA28616, by ONR grant N00014-12-1-0751 under Dr. Ki-Han Kim, by NSF grant CBET 1253157, and through computational resources and services provided by Advanced Research Computing at the University of Michigan, Ann Arbor.

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Correspondence to M. T. Henry de Frahan.

Additional information

This paper is based on work that was presented at the 29th International Symposium on Shock Waves, Madison, Wisconsin, USA, July 14–19, 2013.

Communicated by D. Ranjan.

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Henry de Frahan, M.T., Movahed, P. & Johnsen, E. Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities. Shock Waves 25, 329–345 (2015).

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  • Richtmyer–Meshkov instability
  • Rayleigh–Taylor instability
  • Multifluid
  • Multilayered
  • Discontinuous Galerkin