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

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 rate of the neutronics solution 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 the stability of Picard iteration unless the iterative solution of the subproblem is very efficient, which however has not been addressed in the previous studies.