Mixed singular-regular boundary conditions in multislab radiation transport

Abstract

This article reports a computational method for approximately solving radiation transport problems with anisotropic scattering defined on multislab domains irradiated from one side with a beam of monoenergetic neutral particles. We assume here that the incident beam may have a monodirectional component and a continuously distributed component in angle. We begin by defining the target problem representing the class of radiation transport problems that we are focused on. We then Chandrasekhar decompose the target problem into an uncollided transport problem with left singular boundary conditions and a diffusive transport problem with regular boundary conditions. We perform an analysis of these problems to derive the exact solution of the uncollided transport problem and a discrete ordinates solution in open form to the diffusive transport problem. These solutions are the basis for the definition of a computational method for approximately solving the target problem. We illustrate the numerical accuracy of our method with three basic problems in radiative transfer and neutron transport, and we conclude this article with a discussion and directions for future work.