Abstract We derive an analytical solution for the radiation intensity of scattered photons that is valid from the free-streaming phase immediately after photon emission to the diffusive phase after undergoing multiple scatterings. Assuming isotropic and elastic scattering, we utilize the probability density distribution of scattered photons as formulated by Takahashi et al. By applying Lorentz transformation, the radiation intensity in a fluid moving at relativistic speeds can be computed in any inertial frame, enabling the estimation of radiation energy density, radiation flux, and radiation stress tensor. Although this solution is derived assuming simultaneous and isotropic photon emission in the fluid’s rest frame, it can also be applied to more general emission conditions. The solution remains valid even when the initial photon distribution is spatially or directionally anisotropic, by appropriately summing the fundamental solutions. The validity of the analytical solution is demonstrated through comparisons with Monte Carlo radiation transport calculations. Future studies will address the applicability of the solution to anisotropic and inelastic scattering, as well as to flows with nonuniform distributions.
Takeda et al. (Tue,) studied this question.