  Follow-up observations at high-angular resolution of submillimeter galaxies
showed that the single-dish sources are comprised of a blend of several
galaxies. Consequently, number counts derived from low and high angular
resolution observations are in disagreement. This demonstrates the importance
of resolution effects and the need to have realistic simulations to explore
them. We built a new 2deg^2 simulation of the extragalactic sky from the
far-infrared to the submillimeter. It is based on an updated version of the two
star-formation mode galaxy evolution model. Using global galaxy properties, we
use the abundance matching technique to populate a dark-matter lightcone and
thus simulate the clustering. We produce maps and extract the sources, and show
that the limited angular resolution of single-dish instruments have a strong
impact on (sub)millimeter continuum observations. Taking into account these
resolution effects, we are reproducing a large set of observables, including
number counts, redshift distributions, and cosmic infrared background power
spectra. Our simulation describes consistently the number counts from
single-dish telescopes and interferometers. In particular, at 350 and 500 um,
we find that number counts measured by Herschel between 5 and 50 mJy are biased
towards high values by a factor 2, and that redshift distributions are biased
towards low z. We also show that the clustering has an important impact on the
Herschel pixel histogram used to derive number counts from P(D) analysis.
Finally, we demonstrate that the large number density of red Herschel sources
found in observations but not in models could be an observational artifact
caused by the combination of noise, resolution effects, and the steepness of
color and flux density distributions. Our simulation (SIDES) is available at
http://cesam.lam.fr/sides
