A conservative first-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Abstract

Deterministic transport codes play a fundamental role in the modeling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the Sn method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solves them using non-traditional techniques such as ray tracing. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low potential for optimization, as well as not being conservative. A new method has been developed that traces instead to a set of points on each of a zone's surfaces and computes the currents, before using these to obtain the flux. A comparison between these two ray tracing methods shows significant advantages to the new surface method, including inherent particle conservation, similar convergence rate and increased potential for optimization through ray sharing.