When using dimethyl ether (DME) to fuel diesel engines at high load and speed, applying high amounts of exhaust gas recirculation (EGR) to limit NOX emissions, carbon monoxide (CO) emissions are generally high. To address this issue, the combustion and emission processes in such engines were analyzed with the three-dimensional CFD KIVA3V code. The combustion sub-mechanism (76 species and 375 reactions) was validated by comparing simulated ignition delays and flame velocities to reference data under diesel-like and atmospheric conditions, respectively. In addition, simulated and experimentally determined rate of heat release (RoHR) curves and emission data were compared for a heavy-duty single-cylinder DME engine (displaced volume, 2.02 liters) with DME-adapted piston and nozzle geometries. The simulated RoHR curves captured the main features of the experimentally measured curves, but deviated in the premixed (higher peak) and late combustion phases (too high). The simulated NOX and CO emissions under EGR conditions were predicted well. However, CO emissions were too high under non-EGR conditions, probably because the CFD code does not capture the latest part of the combustion process accurately. Parametric equivalence ratio-temperature distributions (plotted on emission maps of CO, formaldehyde, methane, NO and soot), crank-angle-resolved emissions and RoHR curves indicate that as load and speed increase larger fractions of in-cylinder masses are located in relatively rich regions during the diffusion combustion phase, thus promoting the formation of CO, formaldehyde and methane. Consequently, to reduce these emissions the combustion system must be able to limit the formation of excessively rich conditions during later parts of the diffusion combustion phase, which can be achieved by entraining larger amounts of air in the sprays and adapting the piston bowl geometry to increase flame/air interfaces.