Robust and Efficient Methods in Transient Whole-Core Neutron Transport Calculations

Abstract

Modeling the time-dependent transient behavior of nuclear reactors with high-fidelity pin-resolved detail has increased importance when the operating power of the reactor is increased to improve the economic performance. In previous research, the efficiency of the solution of the steady-state neutron transport equation, which provides the initial condition for the transient, was improved with the development of advanced methods such as the Multilevel-in-Space-and-Energy Diffusion (MSED). However, the application of the MSED method was ultimately limited by numerical instabilities in the presence of cross section feedback. The first objective of this research is to improve the efficiency of the steady-state solution by investigating and eliminating the numerical instability of accelerated neutron transport iterations when there is cross section feedback.

The second objective of the research here is to address the computational costs of performing transient simulations by improving the performance of the Transient Multilevel (TML) method in the MPACT code. Specifically, the run time of the CMFD solver in TML dominates the run time, so a one-group acceleration method is developed and added. Automated time-stepping methods were also not previously available for TML. The research here significantly improves the efficiency of the transient calculation by accelerating the CMFD solver and using adaptive time-stepping methods. Improving the stability and efficiency of the transient whole-core neutron transport calculations is the main significant and original contribution of this work.

The specific contributions of this thesis for the steady-state calculation are the theory, development, and implementation of the nearly-optimally partially converged CMFD (NOPC-CMFD) method and the X-CMFD method in MPACT. As its name suggests, the NOPC-CMFD method stabilizes the iteration scheme by determining and utilizing the nearly-optimal partial convergence of the diffusion solutions. The X-CMFD method is an original method that stabilizes the iteration by applying the feedback at the power iteration level of the low-order diffusion eigenvalue problem. Compared to the default iteration scheme in MPACT, the methods developed here demonstrate the same stability compared to CMFD-accelerated transport iterations in problems without feedback, and reduce the overall run time of the full-core multi-state depletion problem by ∼43%.

The principal original work of this thesis for the transient simulations is the introduction of a one-group CMFD (1GCMFD) acceleration method and the development of adaptive time-stepping methods to further accelerate the TML scheme. The 1GCMFD method is shown to reduce the overall computational time of CMFD by as much as 50% for practical large-scale applications. The adaptive time-stepping method introduced adjusts the time step so that the maximum magnitude of the relative error is smaller than 1% for the applications considered in this research. Other innovative methods include the usage of the Spectral Deferred Correction (SDC) method to solve the point-kinetics equation and the use of Strang Splitting (SS) to replace Lie Splitting for coupling the neutronics and the TH solvers. The implemented SDC method is A-stable for orders up to 8, and the SS addresses the inconsistency between the error and time step size when the time step size is varied.

When the 1GCMFD acceleration and the adaptive methods are applied together, the performance of the TML scheme for the SPERT test 86 problem is reduced by ∼22%, and the maximum magnitude of the relative error is reduced from ~1.8% to ~0.4%, compared to the use of TML with the default parameters.