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 the premixed SI combustion in a constant volume chamber, as well as the CI combustion in 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 computational-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.