In our previous work, combustion flows in a smooth tube are simulated with fixed computational meshes to investigate the auto-ignition and the subsequent deflagration to detonation transition (DDT). In this paper, we use another approach, which is adaptive mesh refinement (AMR) technology, to reproduce above detailed DDT as a pilot study of the further study of three-dimensional (3D) DDT with high resolutions and detailed chemical reaction mechanism. The auto-ignition and DDT are successfully captured by AMR system with a much smaller cost. The results are similar to the previous ones. In this paper especially the formation of precursor shock is discussed in details to present how the piston effect works and why the present initial condition can allow a rapid DDT. It is shown that due to the choice of initial conditions, the flame acceleration process in this work is carried out in a very short time because that the reflected shocks with an adequate strength successfully generate a region with high pressure and another region on the flame tip with a fresh gas of a high density. Subsequently, the pressure accumulation benefits the temperature distribution in the form of shock heating, especially in the boundary layer. An auto ignition triggers the DDT in the heated mixture in front of the flame.
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