Kinetic Simulations of Rayleigh-Taylor Instabilities

TL;DR

This paper presents kinetic simulations of Rayleigh-Taylor instabilities relevant to astrophysics, demonstrating good agreement with analytical predictions in the linear regime and observing complex nonlinear behaviors like mushroom shapes.

Contribution

It introduces a large-scale Direct Simulation Monte Carlo code applied to fluid instabilities, bridging kinetic and hydrodynamic regimes in astrophysical simulations.

Findings

Good agreement with analytic solutions in linear regime

Development of mushroom-shaped structures due to secondary instabilities

Validation of kinetic approach for fluid instability evolution

Abstract

We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is in the linear regime, we compare its position and shape to the analytic prediction. Despite the broadening of the fluid interface we see a good agreement with the analytic solution. At later times we observe the development of a mushroom like shape caused by secondary Kelvin-Helmholtz instabilities as seen in hydrodynamic simulations and consistent with experimental observations.