Continuing the DFG-Subproject titled "Flame Propagation in Inhomogeneous Mixtures with Direct Injection - Large-Eddy Simulation, Model Validation and Analysis". Next phase involves the integration of hydrogen mixtures as the fuel source. The primary objective of this project is to enhance the comprehension of the cause-effect chain underlying cycle-to-cycle variations in spark-ignited internal combustion engines. This endeavor encompasses the intricate transport phenomena inherent in hydrogen-based combustion systems. The ongoing project extension presents challenges that entail refining and advancing models and methodologies tailored for Large-Eddy Simulations (LES) focusing on hydrogen thermo-instabilities and differential diffusion.