A GDI engine operating under lean HOS charge conditions is analysed through numerical simulation and experimental analysis. A laboratory engine exhibiting an optical accessible combustion chamber is considered. The experimental characterisation consists in measurements of the inecylinder pressure and IMEP, pollutants at the exhaust and spectroscopy measurements of the in-chamber OH radicals formation. A 3D CFD engine model, including a properly developed sub-model for the spray dynamics and a flamelet based sub-model for combustion, is properly developed and validated on the ground of experimental data. A good accuracy of the model is demonstrated in predicting the main features of the combustion process. Starting from a MBT single injection case, the engine behaviour under double injection strategies is deeply investigated. The total amount of gasoline is assumed as being equally divided between the two injection events, the first occurring during intake, the second during compression. The main conclusion of the paper is that the rate of heat release is faster if a correct choice is made of both the spark advance and the start of the second injection event prior to ignition, the first one being kept fixed. An optimization procedure is indeed performed through CFD computations to make a choice of the control strategy, at constant injected mass of gasoline. The results of the conducted analysis indicate that, after preparing an homogenous mixture with the first injection during intake, the second one has to be realised just after IVC, and that the spark timing has to be advanced with respect to the single injection case, to achieve improvements of both engine power output and pollutants emission. The mechanism leading to PM formation is mostly related to the wallfilm originating in the piston pit as a consequence of the spray impact and the consequent slower evaporation. The experimental verification of the numerical results also highlights a reduction of cyclic variability