Termination of Picard Iteration for Coupled Neutronics/Thermal-Hydraulics Simulations

TL;DR

This paper analyzes the convergence and stability of Picard iteration in coupled neutronics/thermal-hydraulics simulations, highlighting the importance of adaptive tolerances and over-solving for stability.

Contribution

It introduces an inexact Picard iteration scheme with adaptive tolerance and provides Fourier analysis to understand its convergence behavior.

Findings

Slow neutronics convergence can cause instability in Picard coupling.

Tighter tolerances are needed for stable iteration when neutronics convergence is slow.

Over-solving may be necessary to ensure stability in the iterative process.

Abstract

In this paper, we consider the coupled N/TH problem, in which the termination criterion for the neutronics iteration adopts an adaptive tolerance with respect to the fuel temperature residual at each Picard iteration. We refer to this coupling scheme as the inexact Picard iteration method. Fourier analysis is performed to investigate how the convergence behavior of Picard iteration is influenced by the inexact neutronics solution. It is found that if the convergence of the inner neutronics iteration is slow, Picard coupling may become unstable unless a tighter tolerance is used for the neutronics iteration. Nevertheless, our analysis indicates that a certain amount of over-solving is necessary for maintaining the stability of Picard iteration if the iterative solution of the subproblem is not fast enough. However, this issue has not been addressed in the previous studies.