Transport Synthetic Acceleration for the Solution of the One-Speed Nonclassical Spectral S$_N$ Equations in Slab Geometry

Abstract

The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate nonclassical spectral S$_N$ equations, which can be numerically solved in a deterministic fashion using classical numerical techniques. This paper introduces a transport synthetic acceleration procedure to speed up the iteration scheme for the solution of the monoenergetic slab-geometry nonclassical spectral S$_N$ equations. We present numerical results that confirm the benefit of the acceleration procedure for this class of problems.