Numerical simulation of Faraday waves oscillated by two-frequency forcing

TL;DR

This paper presents a numerical simulation method for Faraday waves driven by two-frequency forcing, successfully reproducing various patterns and validating results against experiments, highlighting the importance of volume conservation in simulations.

Contribution

The paper introduces a particle level-set numerical method for simulating two-frequency forced Faraday waves, accurately reproducing experimental patterns and comparing results with weakly nonlinear analysis.

Findings

Successfully reproduces square, hexagonal, and rhomboidal patterns.

Highlights the importance of volume conservation in simulations.

Provides comparison with weakly nonlinear analysis for rhomboidal states.

Abstract

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, Phys. Rev. Lett. 84, 654 (2000) and Phys. Rev. Lett. 85, 756 (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.