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The present work examines the deformation and breakup of droplets impulsively accelerated by air flow at various conditions including the bag breakup and the sheet thinning regime. The 2D axisymmetric model used to investigate the phenomenon is based on the solution of the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology to track the droplet interface. An adaptive local grid refinement technique is implemented to enhance the accuracy of calculations and achieve lower computational cost, along with a sharpening algorithm to minimize the interface numerical diffusion. The present work aims in quantifying the effect of various numerical aspects such as the effect of a) the VOF discretization scheme and solution algorithm, b) the use of an interface sharpening algorithm, c) the velocity field initialization, and d) the effect of turbulence levels on the droplet deformation. The model performance is assessed by comparing the results against published numerical solutions and experimental data always taking into account the sensitivity of numerical settings on the flow field solution algorithm. It is proved that the model is able to qualitatively capture the breakup regimes, while the numerical settings that best predict the experimental data are identified.