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

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.

💡 Research Summary

This paper revisits the virtual‑density (VD) method for representing uniform geometric perturbations in nuclear reactor physics and couples it with an intrusive generalized polynomial chaos (gPC) approach to obtain a reduced‑order model of the multiplication factor (k‑eff) as a function of the perturbation amplitude. The authors first transform a uniform expansion or swelling of the whole core into an equivalent cross‑section perturbation by applying a coordinate scaling, as originally proposed in the VD theory. This eliminates the need to modify the geometry in a Monte Carlo (MC) simulation and allows geometric changes to be treated exactly as material‑property changes, which are straightforward to handle in MC particle transport.

The core methodological contribution is the integration of intrusive gPC directly into the MC power‑iteration loop. Instead of performing a series of independent MC runs (the non‑intrusive approach) and post‑processing the results, the authors accumulate the gPC coefficients on‑the‑fly during each generation of the power iteration. For a single uncertain parameter X (the normalized perturbation amplitude, assumed uniformly distributed on