The incorporation of detailed chemistry in internal combustion engine (ICE) simulations is challenging due to the large number of chemical species and the wide range of chemical timescales involved, which is further complicated by the highly transient nature of the combustion process. The performance of chemistry acceleration methods such as in situ adaptive tabulation (ISAT) deteriorates dramatically in ICE simulations because of the large variation in the accessed composition space. In this study, a dynamic pruning (DP) strategy for ISAT and an automated initial searching species method together with adaptive reduction thresholds for dynamic adaptive chemistry (DAC) are first proposed to enhance the capabilities of ISAT and DAC for transient ICE simulations, respectively. For ISAT, the dynamic pruning for infrequently accessed tabulated points is achieved by pruning the least recently used tabulated entries. It is observed that DP strategy can improve the computational efficiency in chemistry for the compression and post-combustion stages by an order of magnitude. For DAC, the automated specification of searching-species is based on species reactivity, which is characterized by the species rates of change. The two-stage n-heptane/air autoignition illustrates that it can dynamically select the species of importance according to the progress of the combustion process. The dynamic specification of reduction thresholds based on local thermodynamic conditions can achieve an additional 20% reduction in species and reactions for high-temperature combustion. A static adaptive chemistry acceleration approach is then proposed to further improve the chemistry calculation, in which the enhanced ISAT or DAC is employed at different combustion stages based on the encountered composition inhomogeneity and reaction activity. Specifically, ISAT is employed during the compression and post-combustion stages and DAC is employed during the combustion stage if composition inhomogeneity is significant. It is found that compared to the fixed coupled ISAT-DAC approach, the static adaptive approach can improve the efficiency of chemistry calculations by an order of magnitude for the compression and post-combustion stages and a factor of 2 for the combustion stage. For the simulated HCCI combustion of primary reference fuel with significant composition inhomogeneity, the proposed static adaptive approach achieves a speed-up factor of more than 5 for chemistry calculation with a 171-species mechanism while maintaining accurate predictions of pressure, temperature, and species. It is three time more efficient than the fixed coupled ISAT-DAC approach, demonstrating the great potential of dynamic chemistry acceleration approaches for ICE simulations.