Assessment of numerical methods for the evaluation of higher-order harmonics in diffusion theory

The knowledge of higher-order harmonics besides the fundamental mode is important and useful in the prediction of the spatial behaviour of nuclear reactors. Previous works have evidenced that the information on higher-order modes is of great relevance in the interpretation of flux tilts in large cores. In order to assess the performance of the methods that are available to evaluate such modes in nuclear systems, simple configurations that allow for an analytical solution are analyzed, and the iteration process of filtered power, sub-space iteration and implicitly restarted Arnoldi methods are compared and discussed. The drawbacks of the filtered power method are highlighted. The implicitly restarted Arnoldi method is then chosen as the best approach for the analysis of a full-core realistic configuration, based on the C5G7 benchmark.