Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

The vortex method is applied to simulations of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The numerical results from the vortex method agree well with analytic solutions and other numerical results. The bubble velocity in the RT instability converges to a constant limit, and in the RM instability, the bubble and spike have decaying growth rates, except for the spike of infinite density ratio. For both RT and RM instabilities, bubbles attain constant asymptotic curvatures. It is found that, for the same density ratio, the RT bubble has slightly larger asymptotic curvature than the RM bubble. The vortex sheet strength of the RM interface has different behavior than that of the RT interface. We also examine the validity of theoretical models by comparing the numerical results with theoretical predictions.