An improvement of the double discrete ordinate approximation solution by Laplace technique for radiative-transfer problems without azimuthal symmetry and high degree of anisotropy

Abstract

One-dimensional radiative-transfer problems without azimuthal symmetry and with a high degree of anisotropy are solved using the double discrete ordinate approximation methods LTA N and ALTA N . The discussed methods start with projecting out azimuthal components of the original equation and results in an equation system. Then the collocation method is applied to the polar angle and the integral is approximated by a Gaussian quadrature scheme that yields the S N transport equation system. The subsequent application of the Laplace transform in the spatial variable opens pathways for application of the specific procedures that characterise the LTA N and the ALTA N methods. The results are solutions for the radiative-transport problem. We further report on numerical simulations and comparisons with the LTS N method.