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A continuous multi-component fuel evaporation model has been integrated with an improved G-equation combustion and detailed chemical kinetics model. The integrated code has been successfully used to simulate a gasoline direct injection engine. In the multi-component fuel model, the theory of continuous thermodynamics is used to model the properties and composition of multi-component fuels such as gasoline. In the improved G-equation combustion model a flamelet approach based on the G-equation is used that considers multi-component fuel effects. To precisely calculate the local and instantaneous residual which has a great effect on the laminar flame speed, a “transport equation residual” model is used. A Damkohler number criterion is used to determine the combustion mode in flame containing cells.