In this work, an efficient and unified combustion model is introduced to simulate the flame propagation, diffusion controlled combustion, and chemically driven ignition in both SI and CI engine operation. The unified model is constructed upon a G-equation model which addresses the premixed flame propagation. The concept of the Livengood-Wu Integral is used with tabulated ignition delay data to account for the chemical kinetics which is responsible for the spontaneous ignition of fuel-air mixture. A set of rigorously defined operations are used to couple the evolution of the G scalar field and the Livengood-Wu Integral. The diffusion controlled combustion is simulated equivalent to applying the Burke-Schumann limit. The combined model is tested in the simulation of a swirl-dominant stratified charge GDI engine, as well as a conventional small bore diesel engine. The result shows satisfactory accuracy of the predicted cylinder pressure and heat release rate, while maintaining low computational cost. The combined model provides a natural, robust, and efficient solution to two difficult tasks in development-oriented processing-power-constrained engine simulation: a) to predict SI knock in G-equation simulation; b) to account for the CI induction time in spray combustion simulation at the Burke-Schumann limit.