Shock waves have been recently observed in high-pressure diesel sprays. In this paper, three-dimensional numerical simulations of supersonic diesel spray injection have been performed to investigate the underlying dynamics of the induced shock waves and their interactions with the spray. A Volume-of-Fluid based method in the CFD software (CONVERGE) is used to model this multiphase phenomena. An adaptive Mesh Refinement (AMR) scheme is employed to capture the front of the spray and the shock waves with high fidelity. Simulation results are compared to the available experimental observations to validate the numerical procedure. Parametric studies with different injection and ambient conditions are conducted to examine the effect of these factors on the generation of shock waves and their dynamics.