Kinetic Simulations of Mesoscopic Rayleigh-Taylor Instability

The Rayleigh-Taylor Instability (RTI) is widely observed in nature and engineering, including in non-continuum flows. In Inertial Confinement Fusion (ICF), this “mesoscopic” RTI drives mixing that cools the hot spot. Accordingly, understanding the role of kinetic effects on RTI has been a focus of recent work*.

Fully kinetic simulations of RTI pose a challenge because they must resolve the 6D particle distribution function. We present a numerical method that reduces problem dimension via a spectral expansion of the velocity space onto asymmetrically-weighted Hermite polynomials. In this expansion, the lowest-order terms completely describe the continuum limit, and higher-order terms capture the kinetic effects. In addition to BGK collisions, the method can easily accommodate higher-fidelity models such as Fokker-Planck collisions. The enhanced efficiency and improved collisional physics of the model allow for RTI simulations that better approach ICF conditions.

As a step towards full ICF complexity, we present proof-of-concept single-mode RTI simulations of a neutral fluid with BGK and Fokker-Planck collisions. We discuss our formulation of boundary conditions and collision operators, compare results between collision models over a relevant range of Knudsen and Mach numbers, and connect our findings to related work*.

[*] Majumder, S., Livescu, D., & Girimaji, S. S. (2024). Onset of kinetic effects on Rayleigh–

Taylor instability: Advective–diffusive asymmetry. Physics of Fluids, 36(12).