The demands for extending the limiting operation conditions and enhancing the combustion efficiency of scramjets raise new challenges to the research of reliable robust and controllable flame stabilization in supersonic flows. In the present study, Large Eddy Simulation of flame stabilization in a realistic supersonic combustor, employing the tabulation of dynamic adaptive chemistry (TDAC) method were conducted, in comparisons with other relevant chemistry treatment methods, i.e., dynamic adaptive chemistry (DAC), global skeletal mechanism, and detailed mechanism. The wall pressures, the pseudo one-dimensional metrics, combustor global performance and flame structures are all well reproduced by the DAC/TDAC methods compared with the experimental measurements and the benchmark predictions by the detailed mechanism, while the global skeletal mechanism fails to predict the flame stabilization characteristics. The reason for the discrepancy induced by the skeletal mechanism in the flame stabilization simulation was further illustrated through reaction path analyses. Regarding the computational efficiency, the DAC method shows high efficiency for complex reaction systems, with an almost linear increasing speedup factor with the increase of species number. The TDAC method almost doubly further improves the DAC efficiency. The DAC/TDAC methods show great potential of alleviating the huge computational cost while improving the chemistry fidelity for supersonic combustion especially for flame stabilization modeling. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.