The present study has numerically investigates the vaporization, auto-ignition and combustion processes in the high-pressure and high-temperature conditions encountered in the diesel engine. In the present study, in order to understand the overall spray combustion characteristics of DME fuel as well as to identify the distinctive differences of DME combustion processes compared to conventional hydrocarbon liquid fuels, the sequence of the comparative analysis has been systematically made for DME and n-Heptane liquid fuels. Computations for DME fuel are made for two cases including constant fuel mass flow rate condition and fixed heat release rate. Based on numerical results, the discussions are made for the detailed combustion processes of DME and n-Heptane spray.