Nanohydrodynamics simulations: An atomistic view of the Rayleigh–Taylor instability

Abstract

Nanohydrodynamics simulations, hydrodynamics on the nanometer and nanosecond scale by molecular dynamics simulations for up to 100 million particles, are performed on the latest generation of supercomputers. Such simulations exhibit Rayleigh-Taylor instability, the mixing of a heavy fluid on top of a light in the presence of a gravitational field, initiated by thermal fluctuations at the interface, leading to the chaotic regime in the long-time evolution of the mixing process. The early-time behavior is in general agreement with linear analysis of continuum theory (NavierStokes), and the late-time behavior agrees quantitatively with experimental observations. Nanohydrodynamics provides insights into the turbulent mixing process that are inaccessible to either continuum calculations or to experiment.I n this article it is shown that one can make quantitative investigations of complex chaotic hydrodynamic flows, starting at the most fundamental level of atomic motion by using the latest generation of supercomputers. To do so requires solving the simultaneous Newtonian equations of motion for an enormous number of classical particles, large-scale molecular dynamics (MD), which in effect solves the Liouville equation. Such hydrodynamical simulations by MD are limited to less than a billion atoms for a nanosecond, which means systems in three dimensions are, at most, 1,000 particles wide (hundreds of nanometers); hence, one can characterize hydrodynamic flows at these time and distance scales as ''nanohydrodynamics.'' Recent history in the development of massively parallel computers suggests that MD will not reach the scale of micrometers and microseconds in the foreseeable future (1). Rayleigh-Taylor (RT) InstabilityThe RT instability occurs when a heavy fluid lies on top of a light fluid in the attendance of a gravitational field g; the fluids will subsequently mix in a more-or-less turbulent process. The RT process is the classical example of turbulence and was first investigated by Lord Rayleigh in 1883 (2) and later theoretically investigated by Taylor (3). Its relevance ranges from astrophysical supernova explosions to geophysical formations like salt domes and volcanic islands (4, 5), all the way down to inertial confinement fusion (6) and to the general turbulent mixing of fluids.For these purposes MD simulations have been performed on the well studied RT instability (7) as an example and validation of nanohydrodynamics. RT simulations require a large number of particles in an MD calculation (Fig. 1) to resolve fluid structures at late times and the imposition of an enormous gravitational field to reduce the most unstable wavelength to the nanoscale and to mix the fluids on the nanosecond timescale. This most unstable mode of wavelength (wavenumber, k ϭ 2 ͞ ) must be several times smaller than the width of the simulation cell to develop several bubbles and spikes. From linear stability analysis, the most unstable wavelength decreases with increasing g (8), and thus a value of g Ϸ 1 ϫ 10 10 g Earth is required...

New directions for Rayleigh–Taylor mixing

“…An additional simulation [8], based on an incompressible code, shows agreement with experiment for moderate Schmidt numbers. We also mention our earlier simulations, for example [9], stretching over a number of years, with increasing agreement to experiment, and we mention the particlebased simulation, with mixing rates within the experimental range [10]. These simulations are parameter-free in their agreement with experiment.…”

Algorithm Refinement for Fluctuating Hydrodynamics

“…A heavy fluid sits above a light fluid, and spontaneous microscopic fluctuation at the interface between the fluids leads to turbulent mixing throughout the domain. Kadau and co-workers have recently studied the development of this turbulence at the atomic scale [5,6]. That group's atomistic simulations indicate that thermal fluctuations are an important driver of the behavior of complex flows, certainly at the smallest scales and perhaps at all scales.…”

Computational fluctuating fluid dynamics

“…Specifically, we consider the Rayleigh-Taylor instability, which occurs when a heavy fluid rests upon a light fluid [57], and the KelvinHelmholtz instability that arises from the instability of a shear layer. The importance of fluctuations has recently been highlighted in the study of such instabilities by molecular simulations [31,32].…”

“…Rayleigh-Bernard convection (both single species [63] and mixtures [53]), Kolmogorov flow [5,6,43], RayleighTaylor mixing [31,32], combustion and explosive detonation [40,50], and reaction fronts [46].…”