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

TL;DR

This paper introduces a transport synthetic acceleration method to efficiently solve nonclassical spectral S$_N$ equations in slab geometry, demonstrating improved convergence through numerical validation.

Contribution

The paper develops a novel acceleration technique specifically for nonclassical spectral S$_N$ equations, enhancing deterministic solution efficiency.

Findings

Acceleration improves convergence speed.

Numerical results confirm effectiveness.

Method applicable to slab-geometry problems.

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.