This study deals with the modelling and the simulation of the atomization of an isolated droplet by a high-speed flow. During this phenomenon, two main stages are observed: the aerobreakup of the droplet starting with its flattening to the formation of filaments. The second stage concern the formation of a multitude of reduced sizes droplets. Direct numerical simulations are performed to study the breakup and to provide inaccessible information from experimental process. A multiphase compressible flow is necessary to model this liquid/gas interface problem. While the first stage is mainly due to hydrodynamics forces, the capillary effects have to be included in the model to well predict the fragmentation phenomena during the second stage. The model also insures the mass, momentum and energy conservation and the second law of thermodynamics is respected. An appropriate and specific numerical method involving a new adaptive mesh refinement structure with dual cell-boundary trees has been developed. Results on the atomization of an isolated water column and droplet are presented. Comparison with experiment gives good agreement. For the different atomization steps, essential information on the breakup mechanisms are described. Finally, a cloud of reduced sizes droplets is obtained.