We outline the methodology of simulating common envelope evolution ( CEE ) with the moving-mesh code \sevensize MANGA . We extend \sevensize MANGA to include multiple time-steps . This provides substantial speedups for problems with large dynamic range . We describe the implementation of realistic equations of state relevant in stellar structure and the generation of suitable initial conditions . We then carry out two example simulations of a 2 \textrm { M } _ { \odot } red giant with a 0.36 \textrm { M } _ { \odot } core and a 1 \textrm { M } _ { \odot } companion undergoing CEE for 240 days . In one simulation the red giant is set into corotation with the orbital motion and in the other it is non-rotating . We find that the separation between the companion and red giant core shrinks from 52 \textrm { R } _ { \odot } to 3.6 \textrm { R } _ { \odot } and 3.2 \textrm { R } _ { \odot } respectively , ending with an eccentricity of 0.1 . We also find that 66 and 63 per cent of the envelope mass is ejected . This is higher than in many previous works . Several reasons for this are discussed . These include our inclusion of recombination energy . Our simulations show that putting giants in corotation increases the fraction of mass ejected from the system and results in a larger final orbital separation . We conclude that the entire envelope of the red giant might be ejected during the plunge phase of CEE in this region of parameter space .