Elliptical nozzles are known to provide increased spray angle and lower Sauter mean diameter of droplets, thus resulting in improved fuel-air mixing quality that significantly impacts the combustion efficiency and emissions for modern diesel engines. Numerical simulations play an important role in understanding the breakup process in elliptical nozzles and the effect of different parameters such as aspect ratio, injection pressure, back pressure, etc. on the performance of the nozzles. Generally, large eddy simulations (LES) and volume of fluid (VOF) method are combined to understand the characteristics of the elliptical sprays. However, the resolution of the minimum droplet size is limited by the size of the mesh; therefore, such numerical approaches are difficult to adopt for industrial applications. In the current paper, VOF-to-DPM transitional approach and dynamic unstructured mesh refinement are explored to cut down the simulation cost without affecting the simulation accuracy. VOF method captures the core and the larger droplets while Discrete Phase Model (DPM) captures the smaller droplets using the Subgrid approach. VOF-to-DPM transitional approach converts the droplets from VOF framework to DPM framework conserving mass, momentum, and energy. Since smaller droplets are captured in the Subgrid approach, the overall mesh count requirement is considerably smaller than the pure VOF approach. Dynamic unstructured mesh refinement helps to resolve the VOF interface accurately. At the same time, it keeps the mesh count at a reasonable level. Using these approaches, the mechanism of spray breakup and axis switching of elliptical sprays at different operating conditions is studied and the obtained spray tip penetration and Sauter mean diameters are compared with experimental data.