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International audience; 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. © 2019 Elsevier Ltd

In this work some characteristics of the eigenvalue problem for the neutron transport equations are considered. Various formulations are examined, discussing some theoretical and practical aspects. The standard multiplication eigenvalue that is particularly relevant for nuclear reactor physics applications is analysed, together with the time eigenvalue, including also the contribution of delayed neutrons. In addition, the less common collision and density eigenvalues are also discussed, highlighting interesting physical features. A semianalytical approach is developed allowing to evidence some interesting structures of the eigenvalue spectra. The study is carried out within the spherical harmonics approach. For the plane one dimensional geometry, the mathematical relationship between even and odd-order approximations for the homogeneous form of the equations for the eigenvalue formulation is investigated. It is shown that the even-order system of equations can be re-cast in the form of the contiguous lower odd-order one. Numerical results are obtained in the two-group energy model for various configurations for which a reference is available, providing also results for high-order approximations. The study includes a presentation and discussion of the spectra patterns for the various eigenvalue formulations.