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A storage/retrieval scheme - in situ adaptive tabulation (ISAT) [1] - is used to implement detailed chemistry in a multidimensional engine CFD code. The emphasis is on predicting autoignition in nearly homogeneous and moderately non-homogeneous mixtures (HCCI); preliminary results for highly non-homogeneous direct-injection autoignition also are reported. Speedups approaching a factor of 100 have been realized with ISAT compared to direct integration of the chemical source terms; factors of five-to-ten are more readily obtainable. In the standard ISAT method, table size increases as the square of the number of chemical species in the reaction mechanism; here linear scaling is achieved by limiting the set of independent tabulation variables, while still retaining the full chemical mechanism. A key to effective use of storage/retrieval is judicious specification of the control parameters; guidelines for parameter specification are presented.