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A study of n-dodecane atomization, following the prescribed unseating of the needle tip, is presented for a high-pressure, non-cavitating Bosch Diesel injector (“Spray A”, in the Engine Combustion Network denomination). In the two simulations discussed here, the internal and external multiphase flows are seamlessly calculated across the injection orifice using an interface-capturing approach (for the liquid fuel surface) together with an embedded boundary formulation (for the injector's walls). This setting makes it possible to directly relate the liquid jet spray characteristics (under the assumption of sub-critical flow and with a grid resolution of 3 µm, or 1/30 of the orifice diameter) to the moving internal geometry of the injector. Another novelty is the capability of modeling the compressibility of the liquid and the gas phase while maintaining a sharp interface between the two.