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Atomizing systems must be able to form sprays with predetermined characteristics. There are affected by the shape of the injector as well as external conditions. Thus, in order to avoid numerous experiments, this is necessary to develop predictive atomization models able to deal with the complete atomization process. This can be done using a Eulerian model for primary break-up. This approach describes the flow continuously from inside the injector to the dispersed spray region. In this paper the Eulerian multiphase approach and the Eulerian single-phase approach are compared and the results lead to an intermediate quasi-multiphase approach for describing the spray core. Finally a transition zone permits to represent the diluted spray region by using the classical Lagrangian approach to benefit of the experience accumulated on this method, in particular for the vaporization and the combustion.