Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability

Abstract

A tentative review is presented of various approaches for numerical simulations of two-fluid gaseous mixtures at high density ratios, as they have been applied to the Rayleigh–Taylor instability (RTI). Systems exhibiting such RTI behaviour extend from atomistic sizes to scales where the continuum approximation becomes valid. Each level of description can fit into a hierarchy of theoretical models and the governing equations appropriate for each model, with their assumptions, are presented. In particular, because the compressible to incompressible limit of the Navier–Stokes equations is not unique and understanding compressibility effects in the RTI critically depends on having the appropriate basis for comparison, two relevant incompressible limits are presented. One of these limits has not been considered before. Recent results from RTI simulations, spanning the levels of description presented, are reviewed in connection to the material mixing problem. Owing to the computational limitations, most in-depth RTI results have been obtained for the incompressible case. Two such results, concerning the asymmetry of the mixing and small-scale anisotropy anomaly, as well as the possibility of a mixing transition in the RTI, are surveyed. New lines for further investigation are suggested and it is hoped that bringing together such diverse levels of description may provide new ideas and increased motivation for studying such flows.

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

“…The paper by Livescu [7] attempts to outline approaches for modelling RT/RM mixing-a 'challenge' problem for numerical methods, as has been stated already. The author provides a review of numerical methods available for the description of RTI with an emphasis on configurations at large density ratios.…”

“…This part II of the Theme Issue consists of the following papers: the paper by Sreenivasan & Abarzhi on acceleration and turbulence in Rayleigh-Taylor (RT) mixing [1]; by Meshkov on experimental studies of unstable interfaces [2]; by Youngs on numerical modelling simulations of self-similar regimes in mixing flows [3]; by Grinstein et al [4] on a pragmatic approach for reproducing complex multiphase flows in simulations; by Glimm et al [5] on the so-called alpha problem; by Nevmerzhitskiy on the implementation and diagnostics of RT/Richtmyer-Meshkov (RM) mixing in experiments [6]; by Livescu on high resolution approaches for numerical modelling of RT instabilities [7]; by Statsenko et al [8] on subgrid scale models applied to RT/RM mixing; by Prestridge et al analysing the RM mixing experiments conducted over the past decade [9]; by Levitas on mixing applications in reactive flows [10]; by Pudritz & Kevlahan on supersonic processes and shock waves in interstellar media [11]; and by Anisimov et al [12] summarizing the status of our understanding of RT mixing. We observe the development of the Rayleigh-Taylor instability (RTI) when fluids of different densities are accelerated against the density gradient [13,14].…”

A new framework for simulating forced homogeneous buoyant turbulent flows

“…This type of mixing is often referred to as "two-fluid mixing," and multiple approaches have been used for the numerical simulations of such flows. The reader is referred to [18] for an extensive review. The present work relies on the low Mach number formulation of the Navier-Stokes equations [19,20], which has been used extensively for mixing (including stratified flows) and combustion applications [21][22][23].…”

Nodal Analysis of Nonlinear Behavior of the Instability at a Fluid Interface

“…Note that the exploration of alternate metrics is not specific to the analysis of experimental results like here. It is equally relevant for the many existing results based on the direct numerical simulations of interface instabilities (see, for instance, the recent review article by Livescu [15]). Indeed, just as with experimental observations, the interpretation of numerical simulations requires relevant synthetic descriptors.…”