The Influence of Viscosity on the Oscillations of Superposed Fluids

Harrison, W. J.

doi:10.1112/plms/s2-6.1.396

Cited by 81 publications

(33 citation statements)

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“…Note the relatively good agreement with the numerical results after the few cycles needed to reach the normal mode oscillation. close to the natural frequency predicted by the linear theory (see Reference [60]; note that in this case 1 = 2 ), * = *…”

Section: Standing Gravity and Capillary Waves Of Small Amplitudementioning

confidence: 56%

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On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows

Gómez

Hernández

López

2005

Int. J. Numer. Meth. Engng

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SUMMARYA local level set algorithm for simulating interfacial flows described by the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations are solved using a finitedifference discretization on a Cartesian grid and a second-order approximate projection method. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid, which is reconstructed every time step and refined using a simple uniform cell-splitting operation within the band. Instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band. The influence of different PDE-based reinitialization strategies on the accuracy of the results is investigated. The ability of the proposed method to accurately compute interfacial flows is discussed using different tests, namely the advection of a circle of fluid in two different time-reversed vortex flows, the advection of Zalesak's rotating disk, the propagation of small-amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water, and a classical test of Rayleigh-Taylor instability with and without surface tension effects. The interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method.

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Section: Standing Gravity and Capillary Waves Of Small Amplitudementioning

confidence: 56%

“…From computations carried out in domains with greater depths, the effects of finite depth were found to be negligible. Using a dashed line, we have represented in Figure 11 the decay of the wave amplitude predicted from the normal-mode analysis [60], given by a/ = (a 0 / )e * t * , where…”

Section: Standing Gravity and Capillary Waves Of Small Amplitudementioning

confidence: 99%

On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows

Gómez

Hernández

López

2005

Int. J. Numer. Meth. Engng

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“…To demonstrate the quantitative validity of the MD approach, the early-time growth of an imposed single sinusoidal mode perturbation of the interface with wavelength was compared with analytical results of linear stability analysis based on continuum hydrodynamics (8,25). The amplitude of the disturbance grows as e nt (Fig.…”

Section: Resultsmentioning

confidence: 99%

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

Kadau

Germann

Hadjiconstantinou

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

106

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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...

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“…In scaling his results he used various proportionalities, which when combined gave a densimetric Froude number n as the constant parameter which is an additional useful result. Two more hydrodynamic studies which filled in minor details were those of Harrison (1908) and Lamb (1916). Harrisson included the effects of viscosity and was thus able to calculate the rate of energy dissipation which is determined by the energy input and not the other way round.…”

Section: The Nineteenth Century Hydrodynamicistsmentioning

confidence: 99%

The study of density-stratified flows up to 1945 part 2 Internal waves and interfacial effects

Hinwood

1972

La Houille Blanche

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The Influence of Viscosity on the Oscillations of Superposed Fluids

Cited by 81 publications

References 0 publications

On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows

On the reinitialization procedure in a narrow-band locally refined level set method for interfacial flows

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

The study of density-stratified flows up to 1945 part 2 Internal waves and interfacial effects

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