Uncertainty quantification for criticality problems using non-intrusive and adaptive Polynomial Chaos techniques

Abstract

In this paper we present the implementation and the application of non-intrusive spectral techniques for uncertainty analysis of criticality problems. Spectral techniques can be used to reconstruct stochastic quantities of interest by means of a Fourier-like expansion. Their application to uncertainty propagation problems can be performed in a non-intrusive fashion by evaluating a set of projection integrals that are used to reconstruct the spectral expansion. This can be done either by using standard Monte Carlo integration approaches or by adopting numerical quadrature rules. We present the derivation of a new adaptive quadrature algorithm, based on the definition of a sparse grid, which can be used to reduce the computational cost associated with non-intrusive spectral techniques. This new adaptive algorithm and the Monte Carlo integration alternative are then applied to two reference problems. First, a stochastic multigroup diffusion problem is introduced by considering the microscopic cross-sections of the system to be random quantities. Then a criticality benchmark is defined for which a set of resonance parameters in the resolved region are assumed to be stochastic.