Rayleigh–Taylor shock waves

Olson, Britton J.; Cook, Andrew W.

doi:10.1063/1.2821907

Cited by 40 publications

(25 citation statements)

References 22 publications

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“…The Miranda code has been used extensively for simulating turbulent flows with high Reynolds numbers and multicomponent mixing 6,9,24,25 . Miranda uses a 10 th -order compact differencing scheme for spatial differentiation and a 5-stage, 4…”

Section: B the Miranda Codementioning

confidence: 99%

Large eddy simulation requirements for the Richtmyer-Meshkov instability

Olson

Greenough

2014

Physics of Fluids

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The shock induced mixing of two gases separated by a perturbed interface is investigated through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). In a simulation, physical dissipation of the velocity field and species mass fraction often compete with numerical dissipation arising from the errors of the numerical method. In a DNS the computational mesh resolves all physical gradients of the flow and the relative effect of numerical dissipation is small. In LES, unresolved scales are present and numerical dissipation can have a large impact on the flow, depending on the computational mesh. A suite of simulations explores the space between these two extremes by studying the effects of grid resolution, Reynolds number and numerical method on the mixing process. Results from a DNS are shown using two different codes, which use a high-and low-order numerical method and show convergence in the temporal and spectral dependent quantities associated with mixing. Data from an unresolved, high Reynolds number LES are also presented and include a grid convergence study. A model for an effective viscosity is proposed which allows for an a posteriori analysis of the simulation database that is agnostic to the LES model, numerics, and the physical Reynolds number of the simulation. An analogous approximation for an effective species diffusivity is also presented. This framework is then used to estimate the effective Reynolds number and Schmidt number of future simulations, elucidate the impact of numerical dissipation on the mixing process for an arbitrary numerical method, and provide guidance for resolution requirements of future calculations.

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Section: B the Miranda Codementioning

confidence: 99%

Large eddy simulation requirements for the Richtmyer-Meshkov instability

Olson

Greenough

2014

Physics of Fluids

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“…At larger reference pressures, the initial stratification is reduced, so that the pressure can also be interpreted as a stratification parameter [65,66]. This could lead to some analogies to the rich literature on stably stratified flows; however, within the mixing layer, finite pressure values have clear compressibility effects implications, as they can lead to the formation of shock waves [13]. In addition, the interpretation of pressure as a stratification parameter makes sense only for some particular cases of unperturbed flows (e.g.…”

Section: (C) Continuum Descriptions (I) Navier-stokes Equationsmentioning

confidence: 99%

“…Compressible NS equations solvers, on the other hand, pose their own challenges owing to the very large range of dynamically relevant spatio-temporal scales present in the compressible RTI layer. As recent results suggest [13], besides the intrinsic broad range of turbulent scales, such flow also generates shock waves that further extend the dynamically relevant range of scales. One promising approach for such problems, at least at early to intermediate times, when the turbulence is highly localized, is to use an adaptive mesh refinement technique and such approaches are discussed below.…”

Section: Numerical Solutions To the Governing Equationsmentioning

confidence: 99%

“…Nevertheless, in nitrogen, for example, experimental measurements found values of μ B /μ ≈ 0.8 at moderate temperatures, so that the effects of μ B cannot be neglected. In addition, recent simulations [13] indicate that even the classical RTI with compressible fluids develops shock waves, so that the divergence of velocity is not, in general, small. Similarly, for the conduction coefficient, so far, experimental data are still preferred over kinetic theory calculations.…”

Section: (C) Continuum Descriptions (I) Navier-stokes Equationsmentioning

confidence: 99%

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

Livescu

2013

Phil. Trans. R. Soc. A.

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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.

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“…A somewhat analogous phenomenon has been observed in RayleighTaylor instability. 56 For Rayleigh-Taylor instability, Olson and Cook observed that the acceleration of an interface driven by a constant gravitational field generated shocklets, much in the same way a piston does, which eventually catch up to one another to form a weak shock. Presently, in "heavy-to-light" Richtmyer-Meshkov instability, we observe incipient weak shock waves generated by oscillations in the material contact.…”

Section: A Amplitude and Growth Ratementioning

confidence: 99%

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Ward¹,

Pullin

2011

Physics of Fluids

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We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970) (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related byComparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer's linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.

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Rayleigh–Taylor shock waves

Cited by 40 publications

References 22 publications

Large eddy simulation requirements for the Richtmyer-Meshkov instability

Large eddy simulation requirements for the Richtmyer-Meshkov instability

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

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

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