Solution of the radiative transfer equation by eliminating the anisotropic part within the method of synthetic iteration

Abstract

The numerical solution of the vector radiative transfer equation (VRTE) is possible only by its discretization, which requires elimination of the anisotropic part including all singularities. The discretized VRTE for a turbid medium slab has the unique analytical solution in the matrix form. Number of ordinates for the regular part of the solution is determined by the size of the discretization of the radiance angular distribution to take into account the necessary details of this distribution. Significant acceleration of convergence can be achieved by using the method of synthetic iterations. At the first step, the discrete ordinates method with the elimination of the anisotropic part based on a small-angle modification of the spherical harmonics method is used with a small number of ordinates; that provides a good flux convergence. At the second step the angular distribution is refined in the uniform metric.