In internal combustion engines the injection of high-pressure liquid fuel into a low-pressure gas through a nozzle passage is an important process to atomize the liquid and achieve optimal fuel-air mixing. A Computational Fluid Dynamics (CFD) model is eveloped in the present work to simulate the internal- and external-nozzle flow fields in an integrated way. The model assumes that the flow within and near the nozzle is continuous, and an Eulerian flow solver is developed using the general conservation laws of fluid dynamics. Differences in the thermodynamic states of the liquid and gas phases are modeled with a Stiffened Gas Equation of State (EOS). A practical phase equilibrium solver is developed, and is implemented into the Eulerian flow solver to predict phase changes in the flows - in particular, cavitation of the liquid within the injector nozzle passage. The combined equilibrium solver is applied to single-component and two component flows with one component being non-condensable air. A number of test problems are simulated to verify the numerical methods and validate the proposed models. These include two-phase shock tube problems, a converging-diverging nozzle flow problem, a submerged liquid jet problem, and a cavitating liquid jet problem. (C) 2014 Elsevier Ltd. All rights reserved.