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

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., vol. 400, 2000, pp. 1–32). 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, Perlin & Schultz (J. Fluid Mech., vol. 369, 1998, pp. 273–299), is successfully simulated with the present phase-field method.