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

Abstract:

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.

Keywords:

radiation gas dynamics, atmospheric radiation, radiative transfer, transport equation, aggregation of the spectrum, momentum method

Publication language:russian,
pages:36

Research direction:

Mathematical modelling in actual problems of science and technics