Quasi-singular angular finite element methods in neutron transport problems

An angular finite element technique is used within the integro-differential neutron transport equation. The model is cast into a discrete ordinate form, where a suitable modification induced by the numerical procedure is introduced on removal and scattering cross sections, as well as on the source term. The artificial increase of the scattering term produces a reduction of ray effects. The present paper shows that such a reduction can be remarkably enhanced by an appropriate choice of the shape functions utilized to represent the angular dependence of the neutron flux. Shape functions can be chosen to yield usual spherical harmonics equations; however, they do not allow a discrete ordinate formulation of the equations, owing to their singular behaviour. Therefore, the use of shape functions close to those showing such a singular behaviour is proposed. The technique allows a ray effect reduction as much as desired, through the solution of equations having a discrete ordinate form. Results are presented to enlighten features and performance of the method.