  We have developed a semi-empirical simulation of the extragalactic radio
continuum sky suitable for aiding the design of next generation radio
interferometers such as the Square Kilometre Array (SKA). The emphasis is on
modelling the large-scale cosmological distribution of radio sources rather
than the internal details of individual galaxies. Here we provide a description
of the simulation to accompany the online release of a catalogue of 320 million
simulated radio sources. The simulation covers 20x20 deg^2 - a plausible upper
limit to the instantaneous field of view attainable with future (e.g. SKA)
aperture array technologies - out to redshift z=20, and down to flux density
limits of 10 nJy at 151, 610 MHz, 1.4, 4.86 and 18 GHz. Five distinct source
types are included: radio-quiet AGN, radio-loud AGN of the FRI and FRII
structural classes, and star-forming galaxies, the latter split into
populations of quiescent and starbursting galaxies.
  In our semi-empirical approach, the simulated sources are drawn from observed
(or extrapolated) luminosity functions and grafted onto an underlying dark
matter density field with biases which reflect their measured large-scale
clustering. A numerical Press-Schechter-style filtering of the density field is
used to identify and populate clusters of galaxies. Radio source structures are
built from point source and elliptical sub-components, and for FRI and FRII
sources an orientation-based unification and beaming model is used to partition
flux between the core and extended lobes and hotspots. The simulation output
can be post-processed to achieve more complete agreement with observational
data in the years ahead, with the aim of using these 'idealised skies' in
telescope simulators to optimise the design of the SKA itself (abridged).
