On the Use of the Jacobian-Free Newton Krylov Method to Generate One-Group Discontinuity and Super Homogenization Factors for Full-Core Neutron Diffusion Simulations

Coupled Monte Carlo (MC) and thermal-hydraulic analysis is valuable as a design or reference tool but can be slow, especially when implemented in a Picard iteration. Previous work has developed a novel prediction block to achieve convergence with fewer MC simulations. The prediction works in two stages: (1) a surrogate-like model predicts macroscopic cross sections on the fly and (2) a reduced-order neutronic model predicts the flux response to the updated cross sections. The main challenge with the prediction block is that the reduced-order neutronic model cannot reproduce the spatial flux distribution with high fidelity.

This paper investigates the well-established Jacobian-free Newton Krylov (JFNK) method to preserve equivalency between a homogeneous (nodal diffusion) solution and a high-fidelity transport (MC) solution. Instead of performing multiple computationally consuming MC simulations, the nonlinear iterative approach iterates on correction parameters, e.g., assembly discontinuity factors (ADFs) or super homogenization (SPH) factors, using unexpensive nodal solutions. The JFNK approach does not require additional overhead from the MC solver to generate flux tallies. Further, the approach iterates on diffusion solutions produced directly from a desired code, thus ensuring that the parameters are compatible with that code.

The approach is applied to correct a nodal diffusion solution for a realistic three-dimensional pressurized water reactor core. The results obtained in the paper show that the method is very successful in reproducing the heterogeneous solution (up to 2.5% difference in assembly flux for SPH and 0.3% for ADFs) without needing to modify the source code of the nodal diffusion solver. In addition, the results show that ADFs yield the best agreement and are also stable (i.e., weakly varying) when thermal-hydraulic fields are perturbed.