Convergence acceleration aspects in the solution of the PN neutron transport eigenvalue problem

The solution of the eigenvalue problem for neutron transport is of utmost importance in the field of reactor physics, and represents a challenging problem for numerical models. Different eigenvalue formulations can be identified, each with its own physical significance. The numerical solution of these problems by deterministic methods requires the introduction of approximations, such as the spherical harmonics expansion in PN models, leading to results that depend on the approximations introduced (spatial mesh size, N order, ...). All these results represent, in principle, sequences that can easily profit from acceleration techniques to approach convergence towards the correct value. Such a reference value is estimated, in this work, by the Monte Carlo technique. The Wynn- acceleration method is applied to the various sequences of eigenvalues emerging when tackling the solution of the PN models with different orders and increasing spatial accuracy, in order to obtain more accurate, benchmark-quality results. It is shown that the acceleration can be successfully applied and that the analysis of the results of different acceleration approaches sheds some light on the physical meaning of the numerical approximations.