Modern internal combustion engines rely on a high pressure fuel injection system to deliver the fuel inside the engine. This high pressure fuel injection also results in additional complexities, one of which is the cavitation occurring due to large pressure drops inside the injector. The generation of cavitation pockets inside the injector is known to increase the turbulence locally, affecting the external jet formation. To capture this effect, a specific procedure is needed to study the effect of in-nozzle cavitation on the external jet. In this study, we propose and validate a method to study cavitation as well as the external jet formation using a consistent numerical framework based on interface capturing techniques. This formalism allows the representation of three phases : liquid, air and vapor. Numerical simulations of a cavitating liquid jet for two types of cavitation regimes are presented, namely developing cavitation and super cavitation. Numerical results are compared quantitatively, with the existing experimental measurements from the literature of the velocity field inside the injector, and qualitatively, by comparing the liquid and vapor structures obtained in the experiment and the simulation.