The present contribution falls in the scope of high-frequency combustion instabilities occurring in liquid rocket engines. Under subcritical operating conditions, numerical simulations have to render the effects of acoustic waves on the atomisation of liquid jets since these may impact the stability of the engine. Therefore , the present contribution aims at evaluating the ability of a particular numerical strategy adapted to the simulation of two-phase flows to render these interaction mechanisms. The selected strategy is based on the coupling between a diffuse interface method for the simulation of large liquid structures, and a kinetic-based Eulerian model for the description of droplets. The numerical simulation of an air-assisted liquid jet submitted to a transverse acoustic modulation is performed. The flattening of the liquid core under acoustic constraints is retrieved and induces an intensification of its stripping. In addition, thanks to appropriate coupling source terms, the modification of the spray shape as well as periodic oscillations of droplets are retrieved. The numerical strategy is thus proved to be adapted to deal with atomised liquid jets under transverse acoustic modulation and can be used for future numerical studies of high-frequency combustion instabilities.