Numerical simulation of two-dimensional Faraday waves with phase-field modelling

Takagi, Kentarô; Matsumoto, Takeshi

doi:10.1017/jfm.2011.336

Cited by 23 publications

(30 citation statements)

References 24 publications

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“…They perform analyses in two and three dimensions and their results for the threshold values of the oscillating acceleration amplitude are in good agreement with the Floquet analysis of Kumar and Tuckerman [2]. In order to validate the numerical results of Périnet et al [14] with a different numerical method, Takagi and Matsumoto [15] use a numerical scheme based on the phase-field method. They perform an analysis for both linear and nonlinear regimes.…”

Section: Introductionsupporting

confidence: 53%

“…Their results for the magnitude of the critical acceleration in the linear regimes are in good agreement with those of Périnet et al [14], but, in the nonlinear regime, the comparison of the interface dynamics in their test case, taken from Wright et al [7], is only qualitative due to differences between properties of fluids (densities), the size of the physical domain, and the consideration of viscous effects. Takagi and Matsumoto [15] show that the trends of the interface dynamics is similar in both methods and conclude that their model is able to provide accurate numerical results of the Faraday instability. Other different nonlinear cases are tested and show good agreement with experimental results of Jiang et al [16], in particular, concerning the occurrence of the period tripling of standing waves.…”

Section: Introductionmentioning

confidence: 84%

“…To consider Takagi and Matsumoto [15] results as reference solutions for the 2D Faraday instability, a few points must be well established. First, comparisons in linear regime must go beyond checking in a number of cases the computed values for the critical acceleration.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

et al. 2021

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Faraday instability is a classic problem that occurs due to the relative displacement of the interface that separates two immiscible fluids placed in a closed container under oscillating acceleration parallel to gravity. The interface deformation and the induced flow patterns of this two-phase flow are very complex and numerical simulations could allow a deeper understanding of the dynamics of these systems. Some tests have been performed to establish a reference solution, but further validation is needed in order to ensure the validity of these solutions. In this work, we compare some numerical solutions for the linear and nonlinear regimes using the phase field scheme with predictions obtained using different numerical schemes such as Front Tracking, Volume of Fluid, and Element-based Finite Volume Method. The results show that, in both linear and nonlinear regimes, some important differences in the prediction of the interface dynamics between the methods are observed, and the need to provide a reference numerical solution for future benchmarks is highlighted.

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Section: Introductionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 84%

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Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

et al. 2021

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“…In their numerical simulations and after about ten subharmonic periods, P erinet et al [365] predicted a drastic departure from hexagonal symmetry. A fully nonlinear numerical simulation of 2D Faraday waves between two incompressible and immiscible fluids was performed by Takagi and Matsumoto [367] who adopted the phase-field method developed originally by Jacqmin [368]. In the nonlinear regime, qualitative comparison was made with an earlier vortex-sheet simulation of two-dimensional Faraday waves by Wright et al [21].…”

Section: Three-and Multifrequency Parametric Excitationmentioning

confidence: 99%

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

Ibrahim

2015

Journal of Fluids Engineering

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Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

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“…The parametric instability analysis for the interface of two viscous fluids was studied by Kumar and Tuckerman [7], who found that the effect of large viscosity on the wavelength selection is substantial. The two-dimensional Faraday waves of two inviscid fluids were numerically studied by Wright et al [8], the results were also compared with the fully nonlinear numerical simulation by Takagi and Matusumoto [9]. The instability of Faraday interfacial waves between two weakly viscous layers in a rectangular domain was studied by Hill [10].…”

Section: Introductionmentioning

confidence: 99%

Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally

Liao

2018

Physics of Fluids

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A system of two-dimensional, two coupled Faraday interfacial waves is experimentally observed at the two interfaces of the three layers of fluids (air, pure ethanol and silicon oil) in a sealed Hele-Shaw cell with periodic vertical vibration. The upper and lower Faraday waves coexist: the upper vibrates vertically, but the crests of the lower one oscillate horizontally with unchanged wave height and a frequency equal to the half of the forcing one of the vertically vibrating basin, while the troughs of the lower one always stay in the same place (relative to the basin). Besides, they are strongly coupled: the wave height of the lower Faraday wave is either a linear function (in the case of a fixed forcing frequency) or a parabolic function (in the case of a fixed acceleration amplitude) of that of the upper, with the same wave length. In addition, the upper Faraday wave temporarily loses its smoothness at around t = T /4 and t = 3T /4, where T denotes the wave period, and thus has fundamental difference from the traditional one. To the best of our knowledge, this system of the two coupled Faraday waves has never been reported.

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Numerical simulation of two-dimensional Faraday waves with phase-field modelling

Cited by 23 publications

References 24 publications

Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally

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