  Direct Numerical Simulations of the injection of a pulsed round liquid jet in
a stagnant gas are performed. The Reynolds and Weber numbers and the density
ratio are sufficiently large for reaching a complex high-speed atomization
regime. The Weber number based on grid size is small, an indication that the
simulations are very well resolved. Computations are performed using octree
adaptive mesh refinement using the Basilisk free-code platform, down to a
specified minimum grid size $\Delta$. 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 $d = 3\Delta$ . This non-convergence
arises from the 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 $6 \Delta$. 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.
