On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry

TL;DR

This paper explores the use of the Analytical Discrete Ordinates method to efficiently solve nonclassical transport equations in slab geometry, demonstrating high accuracy with spectral approximation and discussing its limitations.

Contribution

It applies the ADO method to spectral approximations of nonclassical transport equations, showing its effectiveness and analyzing its limitations in slab geometry.

Findings

High accuracy results for test problems

Spectral approximation reproduces classical diffusion solutions

High precision arithmetic may be necessary

Abstract

In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generates, as outcome, a system of equations that have the form of classical transport equations and can therefore be solved by current deterministic algorithms. Thus, the investigation of efficient approaches to solve the nonclassical transport equation is of interest and shall be pursued. This is the case of the ADO method which has been successfully used to solve a wide class of problems in the general area of particle transport. Numerical results are presented for two nonclassical test problems in slab geometry. These nonclassical transport problems are chosen in such way that their solution exactly reproduces the solution of the classical diffusion problem. Very accurate results are obtained for both test problems. However, the use of high precision arithmetic is sometimes required as illustrated in the second test problem. Limitations of the spectral approximation are also analyzed and discussed.