Some high-energy photons are thought to be produced by the inverse Compton scattering process in ultrarelativistic flows, and the high-energy component of spectra in gamma-ray bursts can be interpreted by the process. To examine numerically the trajectory of photons traveling in relativistic jets in detail, a coupled computation method of radiative transport with relativistic hydrodynamics is required. We have developed a three-dimensional code of radiative transport on a background with a relativistic flow using Monte Carlo method. Radiative transfer simulations have been implemented in different inertial frames which are described as a shock rest frame or shock moving frames, and obtained results are compared in the shock rest frame to identify a consistent transformation among different frames. Optical depth τ for every directions agrees among each frame if a time duration of the computation is small enough to resolve photon path close to a shock front with almost the speed of light. Although the obtained results of the direction distribution and the spectrum of the escaped photons from the computational domain in each frame show discrepancies due to different flow velocities, they are identical after Lorentz transforming to the shock rest frame. We found the second peak of energy in the high-energy side of the spectra if the simulation condition is determined to allow the scattering process in the upstream side of the shock, and this peak is formed by the inverse Compton scattering process.
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