单模态Richtmyer-Meshkov不稳定性数值模拟

采用VOF(Volume of Fluid)方法和PPM(Piecewise Parabolic Method)方法,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MVPPM(Multi-Viscous-Fluid Piecewise Parabolic Method)。利用MVPPM对多个具有不同初始扰动振幅的二维和三维单模态RM(Richtmyer-Meshkov)不稳定性模型进行了数值计算,并与理论模型的计算结果进行了比较。结果表明,无论二维还是三维情况,当初始扰动振幅相对于波长较小的时候,计算的扰动振幅和增长率与理论模型的计算结果一致。当初始扰动波长不变而振幅逐渐增大时,界面振幅和增长率也逐渐增大。对于具有相同初始扰动的情况,三维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。

Numerical simulations of the single-mode Richtmyer-Meshkov instability

Adopting the VOF (volume of fluid) methodology and PPM (piecewise parabolic method),a high precision numerical algorithm MVPPM (multi-viscous-fluid piecewise parabolic method) is proposed and applied to the compressible multi-viscous-fluid dynamics problems.Several two and three dimensional single-mode Richtmyer-Meshkov instability models with different amplitude are numerically simulated by MVPPM.Comparisons between numerical and theoretical results show that both two dimensional and three dimensional calculated amplitudes and growth rates of perturbed interface are consistent with the predictions of theory models,when the initial amplitude is relatively small to the initial wavelength.When the wavelength of initial perturbation preserves constant and the initial amplitude increases gradually,the calculated amplitude and growth rate of perturbed interface also increase.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 amplitude,so the effects of nonlinearity and three dimensions play important role in the developing of RM instability.