The liquid and gas flows inside as well as outside a simplex (pressure swirl) atomizer play vital roles with respect to the spray atomization phenomena. In this study, a combined approach is presented, which considers both the internal and external liquid flows of a pressure swirl atomizer for the modeling of spray atomization. A theoretical model based on the volume of fluid (VOF) method is used to model the swirling internal flow and the primary breakup of liquid sheet just outside the orifice. Further, the discrete phase model (DPM) is used to predict the secondary droplet breakup outside the injector. The final results are compared with available experimental data. The VOF method predicts the spray cone angle and breakup length accurately and also depicts the dynamics of air core formation inside the atomizer. It is shown that air core dynamics plays a significant role with respect to the growth of surface instability and flapping phenomena in the liquid sheet. The secondary breakup model employs the Kelvin-Helmholtz Rayleigh-Taylor (KHRT) approach and the droplet size distribution predicted by this approach agrees better with published experimental data than do other available secondary breakup models. © 2020 by Begell House, Inc. www.begellhouse.com