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

TL;DR

This paper presents a fully nonlinear numerical simulation of two-dimensional Faraday waves using a phase-field method, validating against linear theory and capturing complex phenomena like period tripling observed in experiments.

Contribution

The study introduces a phase-field approach with the Cahn-Hilliard equation for simulating nonlinear Faraday waves, successfully reproducing experimental phenomena such as period tripling.

Findings

Validation against linear theory confirms accuracy.

Qualitative agreement with vortex-sheet simulations.

Successful simulation of period tripling state.

Abstract

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 (1999) [J. Comput. Phys., v.155, 96]. Its validation is checked against the linear theory. In a nonlinear regime, qualitative comparison is made with an earlier vortex-sheet simulation of two dimensional Faraday waves by Wright et al. (2000) [J. Fluid Mech., v.400, 1]. The vorticity outside the interface region is studied in this comparison. The period tripling state, which is observed in the quasi-two dimensional experiment by Jiang et al. (1998) [J. Fluid Mech., v.369, 273], is successfully simulated with the present phase-field method.