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Liquid atomisation is an important technical field for a wide range of engineering and industrial applications, particularly in the field of internal combustion engines. In these engines, in fact, the amount of pollutants at the engine-out interface is directly related to the quality of the combustion process, which is in turn determined by the quality of the air-fuel mixture preparation in Direct Injection (DI) engines. As a consequence numerical-experimental research is crucial to their development. Despite the significant amount of research that has been carried out on DI engines simulation, breakup modelling is still a challenge. In this paper we present a new numerical model for multiphase flows that could be particularly suited for liquid jet and droplet breakup simulation. The model is based on a Lattice Boltzmann (LB) solver coupled to a higher order finite difference treatment of the kinetic forces arising from non-ideal interactions (potential energy).