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The continuous pursuit of higher combustion efficiencies, as well as the possible usage of synthetic fuels with different properties than fossil-ones, require reliable and low-cost numerical approaches to support and speed-up engines industrial design. In this context, SI engines operated with homogeneous ultra-lean mixtures both characterized by a classical ignition configuration or equipped with an active prechamber represent the most promising solutions. In this work, for the classical ignition arrangement, a 3DCFD strategy to model the impact of the ignition system type on the CCV is developed using the RANS approach for turbulence modelling. The spark-discharge is modelled through a set of Lagrangian particles, whose velocity is modified with a zero-divergence perturbation at each discharge event, then evolved according to the Simplified Langevin Model (SLM) to simulate stochastic interactions with the surrounding gas flow.