Fuel injectors relevant to aerospace combustors exploit geometrical complexity to generate the aerodynamic forces that atomize the fuel and achieve the fuel air mixing that enhances the combustion process. Detailed experimental analysis of the multiphase flow occurring in these injectors remains a challenge due to the extreme operating conditions, the geometrical complexity, and the challenges posed by dense spray measurements. High-fidelity, first-principles simulation offers an alternative analysis approach. Thus far, such simulations have been restricted to canonical problems with benign operating conditions. In this work, we present and apply a numerical framework that enables the simulation of a realistic multinozzle/swirler injector. This framework leverages the coupled level set and volume-of-fluid methodology for capturing the liquid gas surface, the ghost fluid algorithm for reproducing the surface discontinuity, adaptive mesh refinement for efficiently resolving the surface features, Lagrangian droplet models for treating the smallest droplets, and an embedded boundary algorithm to flexibly handle the geometry. Optimization of this framework on massively parallel systems is discussed and so is its validation using the canonical problems of impinging liquid jets and liquid jet in crossflow. Results from the realistic injector simulations are presented, with emphasis on demonstrating the validity and feasibility of the approach via comparisons with experimental evidence. Moreover, it is shown that for the conditions simulated, the liquid jet atomization inside the swirling flow approximates that of a liquid jet in plain crossflow and that filming on the injector walls is minimal. Comparisons against coarse grid simulations indicate that in the latter case the flow fine scale features are compromised but jet penetration and breakup location are not.