Ray-Effect Mitigation in Discrete Ordinate-Like Angular Finite Element Approximations in Neutron Transport

A generalization is made of a previous phase-space finite element approximation of the second-order form of the one-group, two-dimensional neutron transport equation in x-y geometry. Three angular approximations are formulated and compared: continuous piecewise bilinear finite element, piecewise constant finite element, and discrete ordinate. These are incorporated into a unified formalism of discrete ordinate-like equations, enabling the spatial variables to be treated identically using piecewise linear or bilinear finite elements. The resulting equations are solved iteratively by a weighted conjugate gradient method in an improved version of the computer code FENT. Numerical and analytical comparisons of the angular approximations are made, and it is found that both piecewise bilinear and piecewise constant approximations in angle substantially mitigate ray effects. The mitigation is shown to be associated closely with transformation of the hyperbolic discrete ordinate equations to the elliptic operators of the discrete ordinatelike finite element approximations. This transformation is accompanied by the disappearance of the characteristics along the discrete lines of neutron travel, and, hence, by the appearance of physically artificial derivative terms normal to the lines of neutron streaming. These terms grow with the subdomains of the angular finite elements.