Analysis of Ray-Effect Mitigation Techniques

We analyze three ray-effect mitigation techniques in two-dimensional x-y geometry. In particular, two angular finite element methods, and the modulated P₁-equivalent S₂ method, are analyzed. It is found that these techniques give varying levels of ray-effect mitigation on certain traditional test problems, but all of them yield discrete-ray solutions for a line source in a void. In general, it is shown that any transport angular discretization technique that results in a hyperbolic approximation for the directional gradient operator will yield a discrete-ray solution for a line source in a void. Since the directional gradient operator is in fact hyperbolic, it is not surprising that many discretizations of the operator retain this property. For instance, our results suggest that both continuous and discontinuous angular finite element methods produce hyperbolic approximations. Our main conclusion is that the effectiveness of any hyperbolic ray-effect mitigation technique will necessarily be highly problem dependent. In particular, such techniques must fail in problems that have the most severe ray effects, i.e., those that are "similar" to a line source in a void.