Spray atomization plays a vital role in industrial applications such as aerospace propulsion and pharmaceutical manufacturing. Precise control of droplet size distribution in these processes is essential, for example, in ensuring combustion efficiency in engines or consistent powder characteristics for tablet formulation. However, accurately predicting this distribution remains challenging due factors such as the high cost of experimental testing and limitations of reduced-order phenomenological models. Furthermore, it is often the case that the liquids being atomized are non-Newtonian, where increased rheological complexity from polymers in the liquid makes predicting deformation and break-up even more challenging. Consequently, first-principle based computational modeling offers an attractive alternative by producing physics-based predictions built upon the governing conservation laws. The objective of this work is to advance numerical modeling techniques for complex liquid–gas flows encountered in industrial atomization processes. First, a novel hybrid advection scheme is introduced to model the impact of polymeric stresses on liquid deformation without requiring prohibitively fine mesh resolutions. Second, a high-fidelity simulation framework is developed for an industrial simplex atomizer that incorporates sub-grid scale modeling to suppress non-physical film break-up near the nozzle and yields promising agreement with experimentally measured droplet size distributions. Lastly, a preliminary case study is that combines the work in the previous chapters to examine the impact of viscoleastic stresses at the sub-grid scale by simulating the inflation of a viscoelastic droplet. Together, these developments provide a robust and computationally efficient framework for simulating realistic atomization processes and enhance predictive capabilities.