Quasi-random discrete ordinates method for neutron transport problems

Highlights: • The QRDOM is a new method for the approximation of the solution of the radiative transfer equation. • The central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. • The proposed method has the advantage of providing solutions with mitigated ray effects. • The robustness of the new approach is successfully validated against benchmark problems. - Abstract: The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of the solution of neutron 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 approximate solutions with mitigated ray effect. Application of the QRDOM to neutron transport problems in rectangular domains is discussed in detail. The method is tested against benchmark problems for which DOM solutions are known to suffer from ray effects. Numerical experiments indicate that the QRDOM provides accurate results and that it demands less discrete ordinates per source iteration compared to the classical DOM.