Stability Analysis of Picard Iteration for Coupled Neutronics/Thermal-Hydraulics Simulations

TL;DR

This paper provides a Fourier analysis of Picard iteration in coupled neutronics/thermal-hydraulics simulations, predicting convergence behavior based on physical parameters and deriving an optimal underrelaxation factor.

Contribution

It introduces a formal Fourier analysis for Picard iteration in N/TH coupling and derives theoretical convergence predictions and an optimal relaxation parameter.

Findings

Spectral radius depends on temperature difference, Doppler feedback, scattering ratio, and core height.

Theoretical predictions match numerical experiments.

Optimal underrelaxation factor improves convergence.

Abstract

In this paper, we present a formal Fourier analysis (FA) of Picard iteration for the coupled neutronics/thermal hydraulics (N/TH) problem and derive theoretical predictions for the spectral radius of Picard iteration for such coupled calculations as a function of the temperature difference between the fuel and coolant, temperature coefficients of cross sections (i.e., Doppler feedback), scattering ratio, and core height. An optimal underrelaxation factor is also derived based on the Fourier analysis.