Extreme-scale Simulations of the Rayleigh-Taylor Instability in a Mesoscopic Regime

Resolving kinetic physics in large, fluid-scale problems poses a computational challenge. Accurate simulation requires a careful treatment of the intrinsic scale-coupling between the continuum and out-of-equilibrium regions of the domain. Fully kinetic methods handle this difficulty in a robust way but must balance their out-of-equilibrium accuracy with the expense of resolving the 6D particle distribution function globally.

We present a method that treats the curse of dimensionality via expanding the velocity space in terms of Asymmetrically Weighted Hermite (AWH) bases of adaptive order. This expansion fully describes the mass, momentum, and energy of the flow with just a few compact terms. Higher order terms are added in space and time only where needed to accurately resolve departures from the continuum. Collisional physics are easily incorporated, including both BGK and Fokker-Planck collisions with accurate Prandtl number. Together, our scheme achieves excellent accuracy and performance on a wide variety of fluid-kinetic problems.

Our method is demonstrated on the relevant and difficult problem of the Rayleigh-Taylor Instability (RTI) under the conditions of Inertial Confinement Fusion. We contribute to a recent focus of exploring kinetic effects on RTI with high-fidelity simulations run on LLNL’s El Capitan. We share results on both the neutral-fluid and magnetic RTI, with a focus on exploring new regimes of Knudsen and Mach number and drawing comparisons across varying collision models.