The present study is mainly motivated to investigate the vaporization, auto-ignition and combustion processes in high-pressure engine conditions. In order to realistically simulate the dimethyl ether (DME) spray dynamics and vaporization characteristics in high-pressure and high-temperature environment, the high-pressure vaporization model is utilized. The interaction between chemistry and turbulence is treated by employing the Representative Interaction Flamelet (RIF) model. The detailed chemistry of 336 elementary steps and 78 chemical species is used for the DME/air reaction. Numerical results indicate that the RIF approach, together with the high-pressure vaporization model, successfully predicts the essential feature of ignition and spray combustion processes.