Local analytical discrete ordinate method for the solution of the radiative transfer equation

Abstract

This paper represents a new, accurate approach to solve radiative transfer equation For each discrete ordinates. The radiative transfer equations can be approximated as a linear system of partial differential equations if the source term is averaged within the domain of a finite control volume. Then these equations can be solved analytically by superposition for multi-dimensional problems. Conventional solution (diamond differencing) of the discrete ordinate method (DOM) may lead to negative Fluxes, which is physically unacceptable. The proposed method (local analytical discrete ordinate method, LADOM) does not suffer from such a problem. The predictions of LADOM are well compared with that of zonal and conventional finite-difference methods. The proposed method is more accurate, free from oscillation and simpler to apply to multi-dimensional problems than the conventional finite-difference method.