Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering

TL;DR

The paper introduces the Quasi-Random Discrete Ordinates Method (QRDOM), which enhances classical radiative transfer solutions by reducing ray effects and computational demands through quasi Monte Carlo integration.

Contribution

It proposes a novel QRDOM approach that mitigates ray effects and improves efficiency in solving transport problems with anisotropic scattering.

Findings

QRDOM reduces ray effects compared to classical DOM.

QRDOM achieves accurate results with fewer discrete ordinates.

Numerical tests confirm QRDOM's efficiency and accuracy.

Abstract

The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves the main characteristics of the discrete ordinates method, but it has the advantage of providing mitigated ray effect solutions. The QRDOM is discussed in details for applications to one-group transport problems with isotropic scattering in rectangular domains. The method is tested against benchmark problems for which DOM solutions are known to suffer from the ray effects. The numerical experiments indicate that the QRDOM provides accurate results and it demands less discrete ordinates per source iteration when compared against the classical DOM.