Detailed kinetic reaction mechanisms are necessary for accurate prediction of combustion characteristics such as ignition and emissions in realistic engines. However, the calculation of chemically reacting flows with detailed chemistry is computational expensive due to the large number of species and reactions involved. In this study, a combined approach of dynamic adaptive chemistry (DAC) and in situ adaptive tabulation (ISAT) for efficient chemistry calculations has been implemented into a three-dimensional flow solver to simulate a homogenous charged compression ignition (HCCI) engine with a primary reference fuel (PRF). In the combined method, ISAT speeds up the chemistry calculation by reducing the number of integrations of ordinary differential equations (ODEs) governing chemical kinetics through tabulating and re-using the ODE solutions. At the meantime, DAC accelerates the necessary ODE integrations via the use of locally valid reduced mechanisms, which are obtained using the direct relation graph (DRG) method. The study shows that ISAT-DAC can achieve a speedup factor of about three with accurate prediction of composition and heat release even for the pressure-varying transient engine simulation with significant composition inhomogeneity resulting from wall heat loss. A detailed analysis reveals that the combined method effectively reduces the computational cost through taking advantage of the respective acceleration characteristics of DAC and ISAT at different combustion stages. In the low temperature combustion stage between about 650 K and 1000 K, even though the reduction in the mechanism size and consequently the ODE integration of the chemical kinetics by DAC is not significant, the combined method can still reach a speed-up factor of more than 100 due to the fact that the tabulated entries can effectively be reused. For the high temperature region, even though the tabulated entries cannot be reused due to the rapid change of the pressure and large composition inhomogeneity resulting from the active combustion and heat loss, DAC can effectively reduce the size of the needed ODE integrations by freezing a significant number of unimportant species and reactions. The study further quantifies the effect of composition inhomogeneity on the computation efficiency in detailed chemistry calculations in realistic engine simulations. For the case considered, the temperature inhomogeneity due to the wall heat loss obviously increases at around top dead center (TDC), reaching a level of 350 K difference in temperature within the combustion chamber. Consequently, the overall computational efficiency in chemistry calculation by the combined method has been reduced by 40% compared to the case without heat loss. (C) 2015 Elsevier Ltd. All rights reserved.