In internal combustion engines, the liquid fuel injection is an essential step for the air/fuel mixture preparation and the combustion process. Indeed, the structure of the liquid jet coming out from the injector plays a key role in the proper mixing of the fuel with the gas in the combustion chamber. The present work focuses on the liquid jet atomization phenomena under diesel engine conditions. Under these conditions, liquid jet morphology is assumed, including a separate liquid phase (i.e., a liquid core) and a dispersed liquid phase (i.e., a spray). This article describes the developmental stages of a new atomization model, for a high-speed liquid jet, based on an Eulerian-Eulerian two-fluid approach. The atomization phenomena are modelled by defining different surface density equations for the liquid core and the spray droplets. This new model has been coupled with a turbulent and highly compressible two-fluid system of equations. The process of ligament breakup and its subsequent breakup into droplets are handled by acquiring knowledge from the available high-fidelity experiments and numerical simulations. In the dense region of the liquid jet, the atomization is modelled as a dispersion process due to the stretching of the interface, from the liquid side in addition to the gas side. The model results have been compared to a recently published DNS results under typical direct injection diesel engine conditions. In particular, it has been shown that the interface instabilities and the turbulence in the leading tip of the liquid core play a major role in the primary atomization of diesel jets.