Addressing geometrical perturbations by applying generalized polynomial chaos to virtual density in continuous energy Monte-Carlo power iteration

Abstract

In this work, we revisit the use of the virtual density method to model uniform geometrical perturbations. We propose a general algorithm in order to estimate explicitly the effect of geometrical perturbations in continuous-energy Monte Carlo power iteration simulations. We apply the intrusive generalized polynomial chaos method in order to estimate the coefficients of a reduced model giving the multiplication factor as a function of the amplitude of the geometrical perturbation. Our method accurately estimates the reactivity change induced by uniform expansion or swelling deformations of arbitrary geometries, for a large range of deformations within a single Monte Carlo simulation. The reduced model converges rapidly in polynomial order, does not require knowledge of the adjoint flux, and is free from indirect effects.