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A Smooth Particles Hydrodynamics (SPH) 2D simulation of a twin-fluid atomizer is presented and compared with experiments in the context of bio-fuel production. The configuration consists in an axial high viscosity liquid jet (μl ≈ 0.5 Pa.s) atomized by a coflowing high-speed air stream (ug ≈ 100 m/s) at atmospheric conditions, and the experiment shows two types of jet instability (flapping or pulsating) depending on operating conditions and the nozzle geometry. In order to capture the 3D effects of the axial geometry with a 2D simulation, the surface tension force and the viscosity operator are modified. The mean and RMS velocity profiles of the single phase simulations show a good agreement with the experiment. For multiphase simulations, despite a qualitative good agreement, the type of instabilities as well as its frequency are rarely well captured, highlighting the limitation of 2D geometry in the prediction of 3D configurations.