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 cosm
ological 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).
