The equations for the spectral moments of the distribution function of photons

The expansion of the photons distribution in the system of basic functions depending on the energy of photons is proposed. Regarding the coefficients of the expansion (the spectral moments) formulated a system of moment equations. We find the fundamental solutions of the system. Thus, the problem of solving the kinetic equation of radiative transfer in a substance with a complex absorption coefficient (may contain up to a million of the resonance lines) is reduced to the problem of solving few equations with constant coefficients. It showed a rapid convergence of the expansion to the exact solution on numerical calculations of test problems.
The proposed method is a “method of spectral moments” optimally performs aggregation and recovery of the photon spectrum in the study of problems of radiation gas dynamics and heat transfer, atmospheric radiation.