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The Controlled Auto-Ignition (CAI) combustion, also known as Homogeneous Charge Compression Ignition (HCCI) was achieved by trapping residuals with early exhaust valve closure in conjunction with direct injection. Multi-cycle 3D engine simulations have been carried out for parametric study on four different injection timings, in order to better understand the effects of injection timings on in-cylinder mixing and CAI combustion. The full engine cycle simulation including complete gas exchange and combustion processes was carried out over several cycles in order to obtain the stable cycle for analysis. The combustion models used in the present study are the Shell auto-ignition model and the characteristic-time combustion model, which were modified to take the high level of EGR into consideration. A liquid sheet breakup spray model was used for the droplet breakup processes.