  We introduce a new method for treating Comptonization in computational fluid
dynamics. By construction, this method conserves the number of photons. Whereas
the traditional "blackbody Comptonization" approach assumes that the radiation
is locally a perfect blackbody and therefore uses a single parameter, the
radiation temperature, to describe the radiation, the new "photon-conserving
Comptonization" approach treats the photon gas as a Bose-Einstein fluid and
keeps track of both the radiation temperature and the photon number density. We
have implemented photon-conserving Comptonization in the general relativistic
radiation magnetohydrodynamical code KORAL and we describe its impact on
simulations of mildly super-critical black hole accretion disks. We find that
blackbody Comptonization underestimates the gas and radiation temperature by up
to a factor of two compared to photon-conserving Comptonization. This
discrepancy could be serious when computing spectra. The photon-conserving
simulation indicates that the spectral color correction factor of the escaping
radiation in the funnel region of the disk could be as large as 5.
