Efficient uncertain k_eff computations with the Monte Carlo resolution of generalised Polynomial Chaos based reduced models

In this paper, we are interested in taking into account uncertainties for k_eff computations in neutronics. More generally, the material of this paper can be applied to propagate uncertainties in eigenvalue/eigenvector computations for the linear Boltzmann equation. In the references [1, 2], an intrusive MC solver for the gPC based reduced model of the instationary linear Boltzmann equation has been put forward. The MC-gPC solver presents interesting characteristics (mainly a better efficiency than non-intrusive strategies and spectral convergence): our aim is to recover these characteristics in an eigenvalue/eigenvector estimation context. This is done in practice at the price of few well identified modifications of an existing Monte Carlo implementation. (authors)