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A correct prediction of the initial stages of the combustion process in SI engines is of great importance to understand how local flow conditions, fuel properties, mixture stratification and ignition affect the in-cylinder pressure development and pollutant formation. However, flame kernel growth is governed by many interacting processes including energy transfer from the electrical circuit to the gas phase, interaction between the plasma channel and the flow field, transition between different combustion regimes and gas expansion at very high temperatures. In this work, the authors intend to present a comprehensive, multi-dimensional model that can be used to predict the initial combustion stages in SI engines. In particular, the spark channel is represented by a set of Lagrangian particles where each one of them acts as a single flame kernel.