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

The knowledge of higher-order harmonics beyond 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, by means of perturbation techniques (Gandini, 1978), 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 analysed, and the iteration processes of filtered power, of sub-space iteration and of implicitly restarted Arnoldi methods are compared and discussed. The drawbacks of the filtered power method are highlighted. The implicitly restarted Arnoldi and the sub-space iteration methods are then applied to two benchmarks, the C5G7 and the more realistic UAM configurations, in order to draw some practical indications on their performances. The analysis of the results for all the different configurations considered allow highlighting the better computational performance of the implicitly restarted Arnoldi method as compared to the sub-space iteration method.