Jet atomizations play a crucial role in many applications such as in cryogenic combustion chambers, thus must be thoroughly studied to understand their impact on high-frequency instabilities. Since direct numerical simulations of these two-phase flows in a real configuration of an engine are still out of reach, predictive numerical tools must be developed using reduced-order models. However great care must be taken on the choices of these models in order to both have sound mathematics properties and lead to predictive simulations. The contribution of this work is three-fold. First, we present an original fully Eulerian modelling strategy. It relies on the coupling of a hierarchy of diffuse interface models with a Eulerian kinetic-based moment method (KBMM). Special attention will be given to the description of various disequilibrium levels for the diffuse interface model, which describes the separated and mixed zones. A member of the KBMM hierarchy will accurately describe the polydisperse evaporating spray generated through atomization. Second, to cope with the strong discontinuities encountered in jet atomization, a robust and accurate numerical method using multi-slope MUSCL technique will be applied. The extension of the proposed strategy to the various levels of the diffuse interface models will be discussed. Third, relying on the previous two points, large eddy simulations of a jet atomization in a cryogenic combustion chamber in subcritical conditions are presented using various levels of modelling.