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Considering limited fossil fuel resources and strict limitations of pollutant emissions, the demand for fuel-efficient and environment friendly Internal Combustion Engines (ICE) increases. Homogeneous Charge Compression Ignition (HCCI) engine is of great technological interest as it combines the advantages of both the diesel engine and the spark ignition engine. Firstly, the efficiency of HCCI is comparably high as the diesel engine due to high compression ratios. Secondly, due to strongly diluted and well-mixed charge in the HCCI engine, the emissions of NOx and particulate matter (PM) are reduced. However, HCCI combustion suffers from a lack of control of the ignition process and since high peak pressures and heat releases occur at high loads, the HCCI technology is applied only for a limited operating range. To overcome this issue, strategies are developed to control HCCI combustion which refers to the Controlled Auto Ignition (CAI) concept. The CAI combustion is controlled by the chemical kinetics and highly depends on the properties of the mixture field. Inhomogeneities in the mixture and temperature field designate the combustion characteristics of CAI. Thus, the prediction of the auto-ignition process requires an accurate description of the chemistry within the whole range of thermodynamic conditions given by thermal and composition inhomogeneities. For a better understanding of the chemical and physical phenomena in CAI engines Computational Fluid Dynamics (CFD) is a powerful tool. With regard to a more accurate prediction of situations that intrinsically depend on temporal and spatial variations associated with turbulence, the Large Eddy Simulation (LES) has established as a turbulence modelling approach. Building upon the previous studies, within this work a numerical method to simulate CAI engines is developed. The model consist of the joint application of LES and pre-tabulated auto-ignition chemistry which is implemented into the engine code KIVA-4mpi. The overall numerical framework is verified with zero and one dimensional test cases and applied to a real engine configuration. The dependency of the ignition on scalar quantities being the temperature, air-ratio, Exhaust Gas Recirculation (EGR) and pressure is outlined. Statistical analysis was performed to characterize the strong spatial inhomogeneities within the cylinder. It revealed a strong correlation between the EGR and the temperature as well as two separate branches along which the probability of EGR and the air-ratio evolved. It is demonstrated that the combustion process is pre-determined by these conditions found in the CAI engine. Finally, the analysis of consecutive cycles revealed a strong influence caused by the EGR. It is illustrated that the cycles show non-negligible differences in the ignition delay.