Direct Numerical Simulations of the injection of a pulsed round liquid jet in a stagnant gas are performed in a series of runs of geometrically progressing resolution. 
The  Reynolds and Weber numbers and the density ratio are sufficiently large for reaching a complex high-speed atomization regime but not so large so that the small length scales of the flow are impossible to resolve, except for very small liquid-sheet thickness. 
The Weber number based on grid size is then small, an indication that the simulations are very well resolved. Computations are performed using octree adaptive mesh refinement with a finite volume method and height-function computation of curvature, down to a specified minimum grid size $\mathrm{\Delta }$. Qualitative analysis of the flow and its topology reveal a complex structure of ligaments, sheets, droplets and bubbles that evolve and interact through impacts, ligament breakup, sheet rupture and engulfment of air bubbles in the liquid. A rich gallery of images of entangled structures is produced.  Most processes occurring in this type of atomization are reproduced in detail, except at the instant of thin sheet perforation or breakup.  We analyze drop statistics, showing that as the grid resolution is increased, the small-scale part of the distribution does not converge, and contains a large number of droplets close in order of magnitude to the minimum grid size with a significant peak at $d=3\mathrm{\Delta }$ . 

This non-convergence arises from the {\em numerical sheet breakup} effect, in which the interface becomes rough  just before it breaks.
The rough appearance of the interface is associated to a high-wavenumber oscillation of the curvature.
To recover convergence, we apply the controlled ``manifold death'' numerical procedure, in which thin sheets are detected, and then pierced by fiat before they reach a set critical thickness $h_c$ that is always larger than 
$6\mathrm{\Delta }$. 
This  allows convergence of the droplet frequency above a certain critical diameter $d_c$  above and close to $h_c$. 
A unimodal distribution is observed in the converged range.