Stabilization and convergence acceleration in coupled Monte Carlo-CFD calculations: the Newton method via Monte Carlo perturbation theory

This paper presents the adoption of Monte Carlo Perturbation Theory to approximate the Jacobian matrix of coupled neutronics-thermal/hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton-Krylov (JFNK) methods, that tend to become expensive and inaccurate in presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and demonstrated for a simple 2D PWR case study. (authors)