Quasi-Random Discrete Ordinates Method for Transport Problems

TL;DR

The paper introduces the QRDOM, a novel approach combining quasi Monte Carlo integration with discrete ordinates to reduce ray effects and improve accuracy in transport problem simulations.

Contribution

It proposes the QRDOM, a new method that mitigates ray effects in transport problems by integrating quasi Monte Carlo techniques into the discrete ordinates framework.

Findings

QRDOM provides more accurate solutions than classical DOM.

QRDOM requires fewer discrete ordinates per iteration.

Numerical tests confirm reduced ray effects in benchmark problems.

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.