skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations

Abstract

This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations willmore » be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D{sup FD}) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method.« less

Authors:
 [1]
  1. Nagoya University (Japan)
Publication Date:
OSTI Identifier:
20808479
Resource Type:
Journal Article
Resource Relation:
Journal Name: Nuclear Science and Engineering; Journal Volume: 151; Journal Issue: 3; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; COMPUTER CALCULATIONS; COMPUTERIZED SIMULATION; FOURIER ANALYSIS; MESH GENERATION; NEUTRON TRANSPORT

Citation Formats

Yamamoto, Akio. Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations. United States: N. p., 2005. Web.
Yamamoto, Akio. Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations. United States.
Yamamoto, Akio. Tue . "Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations". United States. doi:.
@article{osti_20808479,
title = {Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations},
author = {Yamamoto, Akio},
abstractNote = {This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations will be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D{sup FD}) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method.},
doi = {},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 151,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • A new nonlinear coarse-mesh rebalance (CMR) method is developed and tested to accelerate the one- and two-dimensional discrete ordinates neutron transport calculations. The method is based on rebalance factors that are angular dependent and defined on the coarse-mesh boundaries only. Unlike the conventional CMR method that is only conditionally stable, Fourier analysis and numerical tests show that this coarse-mesh angular dependent rebalance (CMADR) method is unconditionally stable for any optical thickness, scattering ratio, and coarseness and that the acceleration is very effective in most cases.
  • The NEWTRNX transport module solves the multigroup, discrete-ordinates source-driven or k-eigenvalue transport equation in parallel on a 3-D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slice-balance approach (SBA), spatial discretization. The spatial domains are decomposed using METIS. NEWTRNX is under development for nuclear reactor analysis on computer hardware ranging from clusters to massively parallel machines, like the Cray XT4. Transport methods that rely on full sweeps across the spatial domain have been shown to display poor scaling for thousands of processors. The Parallel Block-Jacobi (PBJ) algorithm allows each spatial partition to sweep over allmore » discrete-ordinate directions and energies independently of all other domains, potentially allowing for much better scaling than possible with full sweeps. The PBJ algorithm has been implemented in NEWTRNX using a Gauss-Seidel iteration in energy and an asynchronous communication by an energy group, such that each partition utilizes the latest boundary solution available for each group before solving the withingroup scattering in a given group. For each energy group, the within-group scattering converges with a generalized minimum residual (GMRES) solver, preconditioned with beta transport synthetic acceleration ({beta}-TSA).« less
  • The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to- spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It ismore » concluded that there is little incentive to use the new methods. (3 tables, 5 figures) (auth)« less
  • The coarse-mesh rebalance method is adopted in Monte Carlo schemes for aiming at accelerating the convergence of a source iteration process to obtain the eigenvalue of a nuclear reactor system. At every completion of the Monte Carlo game for one batch of neutron histories, the scaling factor for the neutron flux is calculated to achieve the neutron balance in each coarse-mesh zone. This rebalance factor is multiplied to the weight of each fission neutron in the coarse-mesh zone for playing the next Monte Carlo game. The numerical examples show that the present rebalance method gives a new usable sampling techniquemore » to get a better estimate of the number of neutrons lost or produced in each coarse- mesh zone by modifying the value obtained directly from the normal Monte Carlo calculation.« less