The CFD model, based on the LANL KIVA-3 computer code, modified to account for the multi-step dimethyl ether, DME/air, oxidation chemistry, was developed and used to study the neat DME combustion dynamics in a constant volume at Diesel-like conditions and in the Volvo AH10A245DI Diesel engine. Constant volume simulations confirm high ignition quality of neat DME in air. The results of engine modeling illustrate that the injection schedule used for Diesel fuel is not optimal for DME. Surprisingly, the positive gain and peak pressure levels comparable with those for Diesel fuel were obtained using an early (∼ -20 ATDC) injection through a nozzle of a larger diameter at reduced injection pressures and velocities (∼150m/s) preventing too rapid spray atomization. At these conditions, combustion heat release has a specific two-stage character with a peak value placed behind the TDC. Thus, application of neat DME requires development of specific fuel injection equipment, FIE, properly matched with the combustion system.