  We present a new subgrid model for neutrino quantum kinetics, which is
primarily designed to incorporate effects of collective neutrino oscillations
into neutrino-radiation-hydrodynamic simulations for core-collapse supernovae
and mergers of compact objects. We approximate the neutrino oscillation term in
quantum kinetic equation by Bhatnagar-Gross-Krook (BGK) relaxation-time
prescription, and the transport equation is directly applicable for classical
neutrino transport schemes. The BGK model is motivated by recent theoretical
indications that non-linear phases of collective neutrino oscillations settle
into quasi-steady structures. We explicitly provide basic equations of the BGK
subgrid model for both multi-angle and moment-based neutrino transport to
facilitate the implementation of the subgrid model in the existing neutrino
transport schemes. We also show the capability of our BGK subgrid model by
comparing to fully quantum kinetic simulations for fast neutrino-flavor
conversion. We find that the overall properties can be well reproduced in the
subgrid model; the error of angular-averaged survival probability of neutrinos
is within $\sim 20 \%$. By identifying the source of error, we also discuss
perspectives to improve the accuracy of the subgrid model.
