  We simulate numerically the full dynamics of Faraday waves in three
dimensions for two incompressible and immiscible viscous fluids. The
Navier-Stokes equations are solved using a finite-difference projection method
coupled with a front-tracking method for the interface between the two fluids.
The domain of calculation is periodic in the horizontal directions and bounded
in the vertical direction by two rigid horizontal plates. The critical
accelerations and wavenumbers, as well as the temporal behaviour at onset are
compared with the results of the linear Floquet analysis of Kumar and Tuckerman
[J. Fluid Mech. 279, 49-68 (1994)]. The finite amplitude results are compared
with the experiments of Kityk et al. [Phys. Rev. E 72, 036209 (2005)]. In
particular we reproduce the detailed spatiotemporal spectrum of both square and
hexagonal patterns within experimental uncertainty.
