Kinetic Simulations of Rayleigh-Taylor Instabilities

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific-heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

Knudsen-number dependence of two-dimensional single-mode Rayleigh-Taylor fluid instabilities

We present a study of single-mode Rayleigh-Taylor instabilities 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 noninteracting gas limit.