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A Large-Eddy Simulation (LES) modeling framework, dedicated to ultra-lean spark-ignition engines, is proposed and validated in the present work. A direct injection research engine is retained as benchmark configuration. The LES model is initially validated using the cold gas-exchange conditions by comparing numerical results with PIV (Particle Imaging Velocimetry) experimental data. Then, the fired configuration is investigated, combining ECFM (Extended Coherent Flame Model) turbulent combustion model with Adaptive Mesh Refinement (AMR). The capability of the model to reproduce experimental pressure envelope and cycle-to-cycle variability is assessed. Within the major scope of the work, a particular focus on the Combustion Cyclic Variability (CCV) is made correlating them with the variability encountered in the in-cylinder aerodynamic variations. R3P4. Finally two post-processing tools, Empirical Mode Decomposition (EMD) and Γ3p function, are proposed and combined to analyse for the first time the aerodynamic tumble-based in-cylinder velocity field. Both tools make it possible to get deeply into the insight and visualization of the flow field and to understand the links between its cyclic variability and the combustion cyclic variability.