Nonoverlapping local/global iterative method for three-dimensional time-dependent neutron transport calculations

Abstract

As modern computing power grows, a whole-core transport calculation becomes more viable. However, the computing time and memory requirement remain major burdens, but the computational burden would be lessened if a proper method is developed to take advantage of a modern parallel computing system. As a candidate for the whole-core transport calculation method, a nonoverlapping local/global iterative method (NLG iteration) has been developed, and the NLG iteration is suitable for the parallel computing system due to the independency of local problems. In this dissertation, the NLG iteration is extended to be capable of transient calculations of 3-D heterogeneous problems. For this purpose, a transient 2-D/1-D fusion transport kernel is developed as the local transport kernel. In addition, the p-CMFD equation is also extended for the transient calculations and it is adopted as the global wrapper in the NLG iteration. 3-D transient problems usually involve the movement scenario of control rods, so a partially rodded node (PRN) needs to be properly homogenized to avoid the rod cusping phenomena. To lessen the rod cusping phenomena, the neighboring spectral index (NSI) weighting method is proposed. The NSI weighting method uses the neighboring spectral indices of a PRN to construct the homogenized cross sections for the PRN. The NSI weighting method is suitable for the 2-D/1-D fusion transport kernel, as the spectral indices are directly obtained during the course of the 2-D/1-D fusion transport calculations in the NLG iteration. As local problems in the NLG iteration is independent of each other, the computationally-expensive local transport calculations by the 2-D/1-D fusion transport kernel are parallelized by using MPI protocol. Therefore, the heavy computational processing and tremendous computing memory requirement can be efficiently distributed over independent parallel computing nodes. In addition, the Predictor-Corrector Quasi-Static (PCQS) method is applied to the NLG iteration to reduce the computing time further consumed in the transient calculations. An adjoint transport solution is required in the PCQS method, and the adjoint transport calculation is computationally-expensive as much as the forward transport calculation. To alleviate this issue, an adjoint p-CMFD equation is derived, and the adjoint transport solution is approximated by the adjoint p-CMFD solution. The parallelized NLG iteration with the PCQS method are implemented in an in-house code, CRX-2K, and several test problems are investigated. Numerical results reveal that the NSI weighting method is accurate enough to capture the rod cusping phenomena, the parallelized NLG iteration has high potential for the whole-core transport calculation, and the computing time consumed in the transient calculations can be reduced significantly by the PCQS method if the reactivity behaves linearly in time for a given time-step size.