  Large-scale diffuse radio emission is observed in some clusters of galaxies.
There is ample of evidence that the emission has its origin in synchrotron
losses of relativistic electrons, accelerated in the course of clusters
mergers. In a cosmological simulation we locate the structure formation shocks
and estimate their radio emission. We proceed as follows: Introducing a novel
approach to identify strong shock fronts in an SPH simulation, we determine the
Mach number as well as the downstream density and temperature in the
MareNostrum Universe simulation which has 2x1024^3 particles in a 500 Mpc/h box
and was carried out with non-radiative physics. Then, we estimate the radio
emission using the formalism derived in Hoeft & Brueggen (2007) and produce
artificial radio maps of massive clusters. Several of our clusters show radio
objects with similar morphology to large-scale radio relics found in the sky,
whereas about half of the clusters show only very little radio emission. In
agreement with observational findings, the maximum diffuse radio emission of
our clusters depends strongly on their X-ray temperature. We find that the
so-called accretion shocks cause only very little radio emission. We conclude
that a moderate efficiency of shock acceleration, namely xi_e <= 0.005, and
moderate magnetic fields in the region of the relics, namely 0.07 to 0.8
muGauss are sufficient to reproduce the number density and luminosity of radio
relics.
