Numerical simulation of Faraday waves oscillated by two-frequency forcing

We perform a numerical simulation of Faraday waves forced with two-frequency oscillations using a level-set method with Lagrangian-particle corrections (particle level-set method). After validating the simulation with the linear stability analysis, we show that square, hexagonal, and rhomboidal patterns are reproduced in agreement with the laboratory experiments [Arbell and Fineberg, Two-mode rhomboidal states in driven surface waves, Phys. Rev. Lett. 84, 654-657 (2000) and Temporally harmonic oscillons in Newtonian fluids, Phys. Rev. Lett. 85, 756-759 (2000)]. We also show that the particle level-set's high degree of conservation of volume is necessary in the simulations. The numerical results of the rhomboidal states are compared with weakly nonlinear analysis. Difficulty in simulating other patterns of the two-frequency forced Faraday waves is discussed. (C) 2015 AIP Publishing LLC.