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Computations were carried out to simulate in-cylinder flow field and mixture preparation of a small port scavenged direct-injection two-stroke spark-ignition engine using a modified version of KIVA-3 code. Simulations of the interaction between air flow and fuel were performed on a commercial Piaggio (125 cc) motorcycle engine modified to operate with a hollow-cone injector located in different positions of the dome-shaped combustion chamber. The engine has a large exhaust port and five smaller transfer ports connecting the cylinder to the crankcase. The numerical grid of this complex geometry was obtained using an IBM grid generator based on the output of engine design by CATIA solution. To take into account the rapid distortion of flow, the standard k-ε turbulence model in KIVA-3 was replaced by the RNG k-ε model.