Simulation of Shock-Induced Hydrodynamic Instabilities Using Particle and Continuum Approaches

Abstract

Shock-induced hydrodynamic instabilities play an important role in a wide variety of applications, ranging from inertial confinement fusion to supersonic combustion systems to astrophysical phenomena [1]. These hydrodynamic instabilities have received relatively little attention in the rarefied regime, even though in such regimes they can arise in micro-scale fuel injection devices [2] or aforementioned astrophysical systems. Thus, better understanding is needed of the role rarefaction plays in the formation and evolution of these instabilities. Whilst the Direct Simulation Monte Carlo (DSMC) method [3] has been shown to be a valid tool for simulation of such phenomena [4, 5], the studies in question focused on the continuum regime, and to the authors knowledge, only few works investigated shock-induced instabilities in the transitional and rarefied regimes [6, 7]. However, in the transitional regime, DSMC can become prohibitively expensive, both in terms of collisions, but also in terms of the requirements on the cell size and timestep (which need to resolve mean free path lengths and mean collision times, respectively), whereas continuum-based approaches do not provide a physically accurate description of the flow physics. In such regimes, the Fokker-Planck approach can be used [8], which avoids direct simulation of collision events, thus greatly reducing the computational cost compared to DSMC simulations. However, the Fokker-Planck method has not yet been applied to simulation of shock-induced instabilities, and its regions of validity (in terms of Knudsen number) and convergence criteria for such problems are not known. In this work, three different methods are applied to simulation of shock-bubble interactions for a variety of Knudsen numbers ranging from the continuum to the rarefied regime: the DSMC method, the particle Fokker-Planck approach, and a continuum based Navier-Stokes-Fourier (NSF) solver. The applicability of the different simulation methods is studied, along with the spatial and temporal resolution requirements.