We mainly focus on the numerical simulation of primary breakup of a high speed jet using a front tracking method. Adaptive Mesh Refinement(AMR) method is used in the simulation, which can speed up the simulation extraordinarily. This work is the extension of Pro. Zhiliang Xu.We do series of simulations to systematically study the parameters used in the cavitation model. With the right choice of parameters, the Sauter mean diameter(SMD) of droplets is in agreement with correlations based on experimental data. We also study the flow in the nozzle, to determine the level of cavitation within the nozzle and of the turbulence occurring at the nozzle exit. We find 2D-3D agreement for the mean velocity field and the occurrence of cavitation, but note some differences in the turbulence levels.To validate the importance of front tracking method in multiphase flow simulation,the primary Rayleigh Instability and Kelvin-Helmholtz Instability are also studied and produce reasonable result.