Five combustion submodels have been improved for modelling gasoline engines with the level set G equation and detailed chemical kinetics. These combustion submodels include a transport equation residual model, the introduction of a Damkohler criterion model for assesing the combustion regime of flame-containing cells, the precise calculation of 'primary heat release' based on the subgrid scale unburned or burned volumes of flame-containing cells, the modelling of flame front quenching in highly stratified mixtures, and a recently developed primary reference fuel (PRF) mechanism. In the transport equation residual model a fictitious species concept is introduced to account for the residual gases in the cylinder, which have a great effect on the laminar flame speed. The residual gases include carbon dioxide (CO2), water (H2O), and nitrogen (N2) remaining from the previous engine cycle or introduced using exhaust gas recirculation (EGR). This pseudo-species is described by a transport equation. The transport equation residual model differentiates between CO2 and H2O from the previous engine cycle or EGR and that which is from the combustion products of the current engine cycle. The Damkohler criterion model is based on a comparison between a laminar flame propagation timescale and the chemical kinetics timescale to determine whether the level set G-equation model or chemical kinetics should be used for assesing the combustion processes in flame-containing cells. The results from implementation of the Damkohler model range between the G-equation model and pure chemistry, depending on the conditions. The improved primary-heat-release calculation model precisely considers the chemical kinetics heat release in unburned regions of flame-containing cells and thus is thought to be physically reasonable. The simulation results show that the flame-front-quenching model effectively captures the flame quench phenomenon on highly stratified mixtures which are typical in gasoline direct-injection engines. Validation of the new PRF mechanism shows that the calculated ignition delay matches shock tube data very well over a wide range of conditions. The integrated model was used to simulate the combustion process in a gasoline turbocharged direct-injection engine, and the same set of combustion model parameters for both high loads and low loads were used. For both high-load and low-load operating conditions, good agreement with the experimental in-cylinder pressure, heat release rates, and mass fraction burned data was obtained.