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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (1): 119-132.doi: https://doi.org/10.1007/s10483-011-1399-x

• Articles • 上一篇    

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

M.A.ULLAH1,2 高文斌1 茅德康1   

  1. 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, University of Chittagong, Chittagong 4331, Bangladesh
  • 收稿日期:2010-08-17 修回日期:2010-12-06 出版日期:2011-01-10 发布日期:2011-01-01

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

 M.A.ULLAH1,2, GAO Wen-Bin1, MAO De-Kang1   

  1. 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, University of Chittagong, Chittagong 4331, Bangladesh
  • Received:2010-08-17 Revised:2010-12-06 Online:2011-01-10 Published:2011-01-01

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摘要： 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.

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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