  The analysis of current and future cosmological surveys of type Ia supernovae
(SNe Ia) at high-redshift depends on the accurate photometric classification of
the SN events detected. Generating realistic simulations of photometric SN
surveys constitutes an essential step for training and testing photometric
classification algorithms, and for correcting biases introduced by selection
effects and contamination arising from core collapse SNe in the photometric SN
Ia samples. We use published SN time-series spectrophotometric templates,
rates, luminosity functions and empirical relationships between SNe and their
host galaxies to construct a framework for simulating photometric SN surveys.
We present this framework in the context of the Dark Energy Survey (DES) 5-year
photometric SN sample, comparing our simulations of DES with the observed DES
transient populations. We demonstrate excellent agreement in many
distributions, including Hubble residuals, between our simulations and data. We
estimate the core collapse fraction expected in the DES SN sample after
selection requirements are applied and before photometric classification. After
testing different modelling choices and astrophysical assumptions underlying
our simulation, we find that the predicted contamination varies from 5.8 to 9.3
per cent, with an average of 7.0 per cent and r.m.s. of 1.1 per cent. Our
simulations are the first to reproduce the observed photometric SN and host
galaxy properties in high-redshift surveys without fine-tuning the input
parameters. The simulation methods presented here will be a critical component
of the cosmology analysis of the DES photometric SN Ia sample: correcting for
biases arising from contamination, and evaluating the associated systematic
uncertainty.
