  We study the phenomenon of the "walking droplet", by means of numerical fluid
dynamics simulations using the Smoothed Particle Hydrodynamics numerical
method. This phenomenon occurs when a millimetric drop is released on the
surface of an oil of the same composition, contained in a tank and subjected to
vertical oscillations of frequency and amplitude very close to the Faraday
instability threshold. At appropriate values of the parameters of the system
under study, the oil droplet jumps permanently on the surface of the vibrating
liquid forming a localized wave-particle system, reminding the behaviour of a
wave particle quantum system as suggested by de Broglie. In our study, we made
relevant simplifying assumptions, however we observe that the wave-drop
coupling is surely obtained. Moreover, the droplet and the wave travel at
nearly constant velocity, as observed in experiments. These facts suggest that
the phenomenon may occur in many contexts and opens the possibility to study it
in an extremely wide range of physical configurations.
