Assessment of the performance of the spectral element method applied to neutron transport problems

The spectral element method can be used to deal with the spatial operators of neutron transport problems with high eciency, as shown recently in the framework of the second-order AN transport approximation. The results highlight interesting computational features and show the appeal of the scheme for reactor physics applications. In this paper we investigate the numerical performance of the method in detail. In order to carry an accurate monitoring of the error behavior to levels close to numerical round-o, we use benchmark problems with known analytical solutions, or with manufactured solutions. Manufactured solutions can easily be obtained for source-injected problems, by tailoring the external neutron source and the boundary conditions to a pre-established analytical solution for a given system. The results presented prove the eectiveness of the method and the high level of accuracy that can be attained.