The common envelope (CE) interaction between a giant star and a lower-mass companion provides a formation channel leading eventually to Type Ia supernovae, sdB stars and bipolar PNe. More broadly, it is an essential ingredient for any population synthesis study including binaries, e.g. cataclysmic variables. Occurring on a short time scale - typically between one and ten years, the CE interaction itself has so far never been observed with certainty but the existence of companions in close orbits around evolved stars, whose precursor's radius was larger than today's orbital separation, vouches for such interaction taking place frequently. Via a detailed study of the energetics and the use of stellar evolution models, we derived in our previous paper the efficiency α of the CE interaction from a carefully selected and statistically analyzed sample of systems thought to be outcomes of a CE interaction. We deduced the initial configuration of those systems using stellar models, and derived a possible inverse dependence of α with the companion to primary mass ratio. Here, we compare these predictions to numerical simulations with two different codes. Enzo is a 3D adaptive mesh refinement grid-based code. For our stellar problem we have modified the way gravity and boundary conditions are treated in this code. The SNSPH code is a 3D hydrodynamics SPH code using tree gravity. The results from both codes for different companion masses and different types of primary stars are consistent with each other. Those results include a resolution study of a 0.88 M<SUB>☉</SUB> red giant interacting with a 0.9, 0.6 and 0.3 M<SUB>☉</SUB> white dwarf, respectively. Those systems reach a final separation of 25, 18 and 10 R<SUB>☉</SUB>, respectively. In this contribution, we present and discuss those results and compare them to our predictions. This research was funded by NSF grant 0607111.