Generalized CoarseMesh Rebalance Method for Acceleration of Neutron Transport Calculations
Abstract
This paper proposes a new acceleration method for neutron transport calculations: the generalized coarsemesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarsemesh rebalance (CMR) and the coarsemesh 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 onegroup 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 »
 Authors:
 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 CoarseMesh Rebalance Method for Acceleration of Neutron Transport Calculations. United States: N. p., 2005.
Web.
Yamamoto, Akio. Generalized CoarseMesh Rebalance Method for Acceleration of Neutron Transport Calculations. United States.
Yamamoto, Akio. Tue .
"Generalized CoarseMesh Rebalance Method for Acceleration of Neutron Transport Calculations". United States.
doi:.
@article{osti_20808479,
title = {Generalized CoarseMesh 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 coarsemesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarsemesh rebalance (CMR) and the coarsemesh 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 onegroup 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 coarsemesh rebalance (CMR) method is developed and tested to accelerate the one and twodimensional discrete ordinates neutron transport calculations. The method is based on rebalance factors that are angular dependent and defined on the coarsemesh boundaries only. Unlike the conventional CMR method that is only conditionally stable, Fourier analysis and numerical tests show that this coarsemesh 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.

Implementation of Generalized CoarseMesh Rebalance of NEWTRNX for Acceleration of Parallel BlockJacobi Transport
The NEWTRNX transport module solves the multigroup, discreteordinates sourcedriven or keigenvalue transport equation in parallel on a 3D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slicebalance 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 BlockJacobi (PBJ) algorithm allows each spatial partition to sweep over allmore » 
Coarsemesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations
The coarsemesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the withingroup scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discreteordinatesto sphericalharmonics fictitious sources used for rayeffect 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 » 
Application of coarsemesh rebalance acceleration to Monte Carlo eigenvalue problems
The coarsemesh 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 coarsemesh zone. This rebalance factor is multiplied to the weight of each fission neutron in the coarsemesh zone for playing the next Monte Carlo game. The numerical examples show that the present rebalance method gives a new usable sampling techniquemore »