Analysis of the Quasi-Transfer Approximation in Problems with Analytical Solution

Abstract

The quasi-transfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this case, it is very important to know the behavior of the correction coefficients, because, for the correctness of the diffusion equation, it is necessary that the diffusion coefficient be positive. This can be verified most easily in problems having analytical solutions. The aim of this work is to study the quasi-transfer approximation in problems with an analytical solution and the behavior of correction coefficients in optically dense and transparent media.