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Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method

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Abstract

This paper presents the numerical simulations of two Richtmyer-Meshkov (RM) instability experiments using the conservative front-tracking method developed in (Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550–1588 (2007)). The numerical results are compared with those obtained in (Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51–64 (1995)). The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, P. R. China

    M. A. Ullah, Wen-bin Gao  (高文斌) & De-kang Mao  (茅德康)

  2. Department of Mathematics, University of Chittagong, Chittagong, 4331, Bangladesh

    M. A. Ullah

Authors
  1. M. A. Ullah
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  2. Wen-bin Gao  (高文斌)
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  3. De-kang Mao  (茅德康)
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Correspondence to De-kang Mao  (茅德康).

Additional information

Project supported by the National Natural Science Foundation of China (No. 10971132) and the Shanghai Pujiang Program (No. [2006]118)

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Ullah, M.A., Gao, Wb. & Mao, Dk. Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method. Appl. Math. Mech.-Engl. Ed. 32, 119–132 (2011). https://doi.org/10.1007/s10483-011-1399-x

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  • DOI: https://doi.org/10.1007/s10483-011-1399-x

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2010 Mathematics Subject Classification

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