Knudsen number dependence of 2D single-mode Rayleigh-Taylor fluid instabilities

TL;DR

This study investigates the dependence of 2D single-mode Rayleigh-Taylor instabilities on the Knudsen number using a modified DSMC simulation approach, revealing how particle mean-free-path influences instability growth and secondary development.

Contribution

It introduces a combined Monte Carlo and Point-of-Closest-Approach method to simulate RTI across a wide range of Knudsen numbers within a single framework.

Findings

Good agreement with linear theory predictions.

Large mean-free-paths suppress secondary instabilities.

Simulations approach non-interacting gas behavior at high Knudsen numbers.

Abstract

We present a study of single-mode Rayleigh-Taylor instabilities (smRTI) with a modified Direct Simulation Monte Carlo (mDSMC) code in two dimensions. The mDSMC code is aimed to capture the dynamics of matter for a large range of Knudsen numbers within one approach. Our method combines the traditional Monte Carlo technique to efficiently propagate particles and the Point-of-Closest-Approach method for high spatial resolution. Simulations are performed using different particle mean-free-paths and we compare the results to linear theory predictions for the growth rate including diffusion and viscosity. We find good agreement between theoretical predictions and simulations and, at late times, observe the development of secondary instabilities, similar to hydrodynamic simulations and experiments. Large mean-free-paths favor particle diffusion, reduce the occurrence of secondary instabilities and approach the non-interacting gas limit.