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Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks

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Abstract

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov(RM) instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

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Authors and Affiliations

  1. LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China

    Baolin Tian, Dexun Fu & Yanwen Ma

  2. Institute of Applied Physics and Computational Mathematics,  , Beijing, 100088, China

    Baolin Tian

Authors
  1. Baolin Tian
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  2. Dexun Fu
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  3. Yanwen Ma
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Corresponding author

Correspondence to Dexun Fu.

Additional information

The project supported by the National Natural Science Foundation of China (10176033, 10135010 and 90205025). The English text was polished by Yunming Chen.

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Tian, B., Fu, D. & Ma, Y. Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks. ACTA MECH SINICA 22, 9–16 (2006). https://doi.org/10.1007/s10409-005-0083-1

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  • DOI: https://doi.org/10.1007/s10409-005-0083-1

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