Numerical simulation of injectors could help improving their designs. In particular, a two-phase flow simulation of a swirl simplex atomizer allows computing the main characteristic parameters such as the spray cone angle, the fuel sheet thickness and the air core diameter. This work describes an attempt to go a step further to characterize atomization and spray characteristics with the ultimate goal to predict the spray distribution in terms of size and velocity. A commercial injector has been used in the CORIA Rouen Spray Burner (CRSB) set up to study turbulent spray combustion. This experiment has produced a well-documented database for the last two TCS workshops (see TCS 6 and 7 at http://www.tcs-workshop.org/). Even though spray measurements are used to define the fuel injection in combustion numerical simulations, the spray injection characteristics remain the main cause of uncertainties. The present work aims at answering this question: Is it possible to complete our knowledge of spray injection by numerical simulation of the full atomization process? The first challenge is to measure the inner geometry. Standards techniques such as X-ray tomography and microscopy have been applied. In order to accurately reproduce the internal throat and swirl chamber, additional measurements have been performed by silicon molding, leading to the definition of a nominal geometry that can be used for further CFD simulation. The second challenge is to produce a mesh regular enough to be compatible with the interface capturing method. Several mesh strategies have been tested starting from the swirl chamber with very thin mesh layers to capture the liquid film at the injector wall and to describe the external liquid sheet. Then, a third challenge concerns the numerical simulation itself, since it must handle the multi-scale nature of such flows until the formation of the spray. A nonreactive condition has been tested with the interFoam solver (OpenFOAM library) in a Large Eddy Simulation (LES) framework. Eventually, the last challenge is to build an analysis to connect the numerical simulation that is limited to the close vicinity of the injector and the experimental measurements that are rejected farther downstream on the dispersed spray. This last step is based on the analysis of the surface curvature distribution that is described with more detail on another presentation at this ICLASS conference.