This work describes the development of a transported Livengood-Wu (L-W) integral model for computational fluid dynamics (CFD) simulation to predict auto-ignition and engine knock tendency. The currently employed L-W integral model considers both single-stage and two-stage ignition processes, thus can be generally applied to different fuels such as paraffin, olefin, aromatics and alcohol. The model implementation is first validated in simulations of homogeneous charge compression ignition combustion for three different fuels, showing good accuracy in prediction of auto-ignition timing for fuels with either single-stage or two-stage ignition characteristics. Then, the L-W integral model is coupled with G-equation model to indicate end-gas auto-ignition and knock tendency in CFD simulations of a direct-injection spark-ignition engine. This modeling approach is about 10 times more efficient than the ones that based on detailed chemistry calculation and pressure oscillation analysis. Two fuels with same Research Octane Number (RON) but different octane sensitivity are studied, namely Co-Optima Alkylate and Co-Optima E30. Feed-forward neural network model in conjunction with multi-variable minimization technique is used to generate fuel surrogates with targets of matched RON, octane sensitivity and ethanol content. The CFD model is validated against experimental data in terms of pressure traces and heat release rate for both fuels under a wide range of operating conditions. The knock tendency — indicated by the fuel energy contained in the auto-ignited region — of the two fuels at different load conditions correlates well with the experimental results and the fuel octane sensitivity, implying the current knock modeling approach can capture the octane sensitivity effect and can be applied to further investigation on composition of octane sensitivity.