Intake, mixing, and combustion processes are simulated in a direct-injection gasoline engine for three substantially different running conditions, including two full loads with homogeneous charge combustion and a part load with stratified charge combustion. The turbulent Flame Speed Closure (FSC) model is implemented into the FIRE code for the three-dimensional simulations of the combustion processes, which is the focus in the present paper. To take local mixture properties into account, a complex chemistry mechanism consisting of 100 species and 475 reactions is used to calculate the laminar flame speeds and chemical timescales required by the model. A large range of equivalence ratios, pressures, and temperatures are investigated and the combustion limits are determined. The FSC model is extended to capture the postflame oxidation between excess fuel from the rich mixture and excess air from the lean mixture. The modeling of the flow field, mixture composition, and combustion is compared with optical and pressure measurements in a test-rig engine showing good agreement. The simulation of the stratified charge combustion indicates that the major part of the unburned fuel after the combustion originates from the lean mixture. The calculated amount of unburned fuel is in good agreement with the measured HC emissions.