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This paper presents three approaches that can be used for efficient multidimensional simulations of HCCI and DI engine combustion. The first approach uses a newly developed Adaptive Multi-grid Chemistry (AMC) model. The AMC model allows a fine mesh to be used to provide adequate resolution for the spray simulation, while dramatically reducing the number of cells that need to be computed by the chemistry solver. The model has been implemented into the KIVA3v2-CHEMKIN code and it was found that computer time was reduced by a factor of ten for HCCI cases and a factor of three to four for DI cases without losing prediction accuracy. The simulation results were compared with experimental data obtained from a Honda engine operated with n-heptane under HCCI conditions for which directly measured in-cylinder temperature and H2O mole fraction data are available.