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

@article{Takagi2011NumericalSO,
  title={Numerical simulation of two-dimensional Faraday waves with phase-field modelling},
  author={Kentaro Takagi and Takeshi Matsumoto},
  journal={Journal of Fluid Mechanics},
  year={2011},
  volume={686},
  pages={409 - 425}
}
Abstract A fully nonlinear numerical simulation of two-dimensional Faraday waves between two incompressible and immiscible fluids is performed by adopting the phase-field method with the Cahn–Hilliard equation due to Jacqmin (J. Comput. Phys., vol. 155, 1999, pp. 96–127). Its validation is checked against the linear theory. In the nonlinear regime, qualitative comparison is made with an earlier vortex-sheet simulation of two-dimensional Faraday waves by Wright, Yon & Pozrikidis (J. Fluid Mech… 
Comparison of Different Numerical Interface Capturing Methods for the Simulation of Faraday Waves
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
Effect of depth on the properties of two coupled Faraday waves in a Hele-Shaw cell
A new type of coupled Faraday wave appears in the system of two immiscible incompressible viscous liquid layers with a free surface filling in a Hele-Shaw cell under vertical oscillation [X. Li, X.
Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate
We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the
Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally
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
Faraday instability of binary miscible/immiscible fluids with phase field approach
The objective of the present work is to model the continuous passage of a binary fluid mixture from its immiscible state into a miscible one. This is achieved with a phase field model using an
The onset and saturation of the Faraday instability in miscible fluids in a rotating environment
must not spill onto p.2 ar X iv :2 20 7. 13 73 9v 1 [ ph ys ic s. fl udy n] 2 7 Ju l 2 02 2 2 Gollub 1989; Douady 1990; Müller 1993; Edwards & Fauve 1994; Binks & van de Water 1997; Kudrolli et al.
...
...

References

SHOWING 1-10 OF 27 REFERENCES
Numerical simulation of Faraday waves
We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference
Numerical studies of two-dimensional Faraday oscillations of inviscid fluids
The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed
A numerical analysis of the influence of the liquid depth on two-dimensional Faraday waves
In this work a numerical analysis of two-dimensional Faraday waves is presented. This study is based on direct numerical simulation of Navier–Stokes and continuity equations with appropriate boundary
Two-dimensional direct numerical simulation of parametrically excited surface waves in viscous fluid
Standing surface waves on a viscous fluid driven parametrically by a vertical harmonic oscillation are investigated, based on direct numerical simulations of the two-dimensional Navier–Stokes
Phase-field model for the Rayleigh–Taylor instability of immiscible fluids
The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method, the sharp fluid interface is replaced
Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling
Phase-field models provide a way to model fluid interfaces as having finite thickness. This can allow the computation of interface movement and deformation on fixed grids. This paper applies
Parametric instability of the interface between two fluids
The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem for
Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops.
TLDR
The Faraday instability in domains with flexible boundaries is studied by triggering this instability in floating fluid drops by coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached.
Dissipative solitary states in driven surface waves.
TLDR
These structures, harmonically coupled to the external driving frequency, are observed above a critical ratio of the viscous boundary layer height to the depth of the fluid layer for a wide range of fluid viscosities and system parameters.
Contact-line dynamics of a diffuse fluid interface
  • D. Jacqmin
  • Engineering
    Journal of Fluid Mechanics
  • 2000
An investigation is made into the moving contact line dynamics of a Cahn–Hilliard–van der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can
...
...