Determination of the reactor kinetic characteristics is very important for the design and development of a new reactor system. In this sense, the computation of lambda modes associated to a nuclear power reactor has interest since these modes can be used to analyze the reactor criticality and to develop modal methods to analyze transient situations in the reactor. In this paper, the lambda problem has been discretized using a high order finite element method to obtain a generalized algebraic eigenvalue problem. A multilevel method is proposed to solve this generalized eigenvalue problem combining a hierarchy of meshes with a Modified Block Newton method. The Krylov-Schur method is used to compare the efficiency of the multilevel method solving several benchmark problems.

The mechanical vibrations of core internals such as fuel assemblies (FAs) cause oscillations in the neutron flux that require in some circumstances nuclear power plants to operate at a reduced power level. This work simulates and analyzes the changes of the neutron flux throughout a nuclear core due to the oscillation of a single FA without considering thermal-hydraulic feedback. The amplitude of the FA vibration is bounded to a few millimeters, and this implies the use of fine meshes and accurate numerical solvers due to the different scales of the problem. The results of the simulations show a main oscillation of the neutron flux with the same frequency as the FA vibration along with other harmonics at multiples of the vibration frequency much smaller in amplitude. Also, this work compares time domain analysis and frequency domain analysis of the mechanical vibrations. Numerical results show a close match between these two approaches for the fundamental frequency.