  We developed a three-dimensional radiative transfer code for an
ultra-relativistic background flow-field by using the Monte Carlo (MC) method
in the context of gamma-ray burst (GRB) emission. For obtaining reliable
simulation results in the coupled computation of MC radiation transport with
relativistic hydrodynamics which can reproduce GRB emission, we validated
radiative transfer computation in the ultra-relativistic regime and assessed
the appropriate simulation conditions. The radiative transfer code was
validated through two test calculations: (1) computing in different inertial
frames and (2) computing in flow-fields with discontinuous and smeared shock
fronts. The simulation results of the angular distribution and spectrum were
compared among three different inertial frames and in good agreement with each
other. If the time duration for updating the flow-field was sufficiently small
to resolve a mean free path of a photon into ten steps, the results were
thoroughly converged. The spectrum computed in the flow-field with a
discontinuous shock front obeyed a power-law in frequency whose index was
positive in the range from 1 to 10 MeV. The number of photons in the
high-energy side decreased with the smeared shock front because the photons
were less scattered immediately behind the shock wave due to the small electron
number density. The large optical depth near the shock front was needed for
obtaining high-energy photons through bulk Compton scattering. Even
one-dimensional structure of the shock wave could affect the results of
radiation transport computation.
