The reduced kinetics model for the low temperature oxidation and the fluid dynamics model were combined to analyze the autoignition sites. The original reduced kinetics model in the literature was modified to express a strong heat release rate on autoignition. A compression ignition of a homogeneous fuel-air mixture in a rapid compression machine was analyzed by a laminar flow computation with boundary layer resolution The computational analysis shows that the outer region of the thermal boundary layer comes to the first autoignition when it stays longer during the end phase of compression in the negative temperature dependence region of the low temperature oxidation reaction. Further analysis was made for the compression of a turbulent field simulated by a random motion flow, solving the spatially filtered transport equations. The results demonstrate that several autoignition spots appear in the numerical cells within 1 mm from the walls. The result suggests that gas blobs in the near wall region have more possibilities to stay longer in the negative temperature dependence regime while hitting the wall and losing heat in the random motion. These analyses give a plausible and reasonable explanation for the experimental evidence that the autoignition sites were often observed in close vicinity to the combustion chamber walls.