A twin-fluid atomizer configuration is predicted by means of the 2D weakly-compressible Smooth Particle Hydrodynamics (SPH) method and compared to experiments. The setup consists of an axial liquid jet fragmented by a co-flowing high-speed air stream (Ug ~ 60 m/s) in a pressurized atmosphere up to 11 bar (abs.). Two types of liquid are investigated: a viscous Newtonian liquid (µ = 200 mPa.s) obtained with a glycerol/water mixture and a viscous non-Newtonian liquid (µ ~ 150 mPa.s) obtained with a carboxymethyl cellulose (CMC) solution. 3D effects are taken into account in the 2D code by introducing (i) a surface tension term, (ii) a cylindrical viscosity operator and (iii) a modified velocity accounting for the divergence of the volume in the radial direction. The numerical results at high pressure show a good qualitative agreement with experiment, i.e. a correct transition of the atomization regimes with regard to the pressure, and similar dynamics and length scales of the generated ligaments. The predicted frequency of the Kelvin-Helmholtz instability needs a correction factor of 2 to be globally well recovered with the Newtonian l ... mehriquid. The simulation of the non-Newtonian liquid at high pressure shows a similar breakup regime with finer droplets compared to Newtonian liquids while the simulation at atmospheric pressure shows an apparent viscosity similar to the experiment.