In this work, we use Direct Numerical Simulation (DNS) through a Volume of Fluid (VOF) solver with Adaptive Mesh Refinement (AMR) to analyze the atomization of a pulsating round liquid jet with a narrow length scale range configuration. We propose three grid sizes based on characteristic scales we estimate from the deformation and fragmentation processes of this problem. We compute drop statistics and general spray features for each case. We found that mesh resolution affects the atomization rate and the probability density function of droplets size and position, not only for the under-resolved drops but all liquid structures. The two simulations with higher grid refinement presented volume-weighted distribution with minor differences. Therefore, we propose assessing the accuracy of atomization simulations based on the volume fraction of under-resolved structures.