A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

Abstract

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS N ) methods applied to the radiative transfer equation in the discrete ordinates (S N ) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S N problems by using the LTS N method. We show some numerical experiments for a typical model problem.