中文摘要：

发展了可用于可压缩多介质粘性流体动力学问题的数值模拟方法和代码MVPPM（Multi-Viscous-FluidPiecewiseParabolicMethod）。利用MVPPM方法对多个具有不同初始扰动振幅和波长的二维和三维单模态Richtmyer—Meshkov（RM）不稳定性模型进行了数值计算，并和理论模型的计算结果进行了比较。结果显示，扰动界面的发展与扰动的初始条件密切相关。无论二维还是三维情况，当初始扰动强度较小的时候，数值计算的扰动振幅及增长率和理论模型的计算结果一致。对于具有相同初始扰动的情况，三维数值计算结果在线性段与二维计算结果相同，但是在非线性段比二维结果大，说明非线性和三维效应在RM不稳定性发展过程中起着重要作用。

英文摘要：

A high precision numerical algorithm MVPPM （multi-viscous-fluid piecewise parabolic method） is proposed and applied to the multi-viscous-fluid dynamics problems. Several two and three dimensional single- mode Richtmyer-Meshkov instability models with different amplitude and wavelength are numerically simulated by this method. Comparisons show that the evolving of interface is highly sensitive to the initial conditions of perturbation. Both two and three dimensional calculated amplitudes and growth rates of perturbed interface are consistent with the predictions of theoretical models, while the strength of initial perturbation is small. The three dimensional numerical results are identical with the two dimensional ones at the linear stage and larger than the two dimensional ones at the nonlinear stage for the perturbation with the same wavelength and ampli- tude. Therefore the effects of nonlinearity and three dimensions play a dominant role in the development of Richtmyer-Meshkov instability.