This article presents a SPH study of a liquid jet break-up, the control of which is improved by applying external vibrations. The numerical method is simple: a standard weakly compressible SPH approach where the gaseous phase is neglected. The density calculation near the free surface is based on an improved geometrical method, which was previously published by the authors. The later allows one to increase the stability of the simulations and thus to widen the range of parameters (We and Oh) compared with previous studies based on SPH. The simulation results show the capability of this approach to simulate the jet break-up phenomenon accurately. This study is a step forward, toward the simulation of liquid atomization in industrial conditions with the SPH method.