  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.
