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A dense-particle Eulerian-Lagrangian stochastic methodology, able to resolve the dense spray formed at the nozzle exit has been applied to the simulation of evaporating diesel sprays. Local grid refinement at the area where the spray evolves allows use of cells having sizes from 0.6 down to 0.075mm. Mass, momentum and energy source terms between the two phases are spatially distributed to cells found within a distance from the droplet centre; this has allowed for grid-independent interaction between the Eulerian and the Lagrangian phases to be reached. Additionally, various models simulating the physical processes taking place during the development of sprays are considered. The cavitating nozzle flow is used to estimate the injection velocity of the liquid while its effect on the spray formation is considered through an atomisation model predicting the initial droplet size.