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Title: Nonlinear Acceleration Methods for Even-Parity Neutron Transport

Abstract

Convergence acceleration methods for even-parity transport were developed that have the potential to speed up transport calculations and provide a natural avenue for an implicitly coupled multiphysics code. An investigation was performed into the acceleration properties of the introduction of a nonlinear quasi-diffusion-like tensor in linear and nonlinear solution schemes. Using the tensor reduced matrix as a preconditioner for the conjugate gradients method proves highly efficient and effective. The results for the linear and nonlinear case serve as the basis for further research into the application in a full three-dimensional spherical-harmonics even-parity transport code. Once moved into the nonlinear solution scheme, the implicit coupling of the convergence accelerated transport method into codes for other physics can be done seamlessly, providing an efficient, fully implicitly coupled multiphysics code with high order transport.

Authors:
; ;
Publication Date:
Research Org.:
Idaho National Laboratory (INL)
Sponsoring Org.:
USDOE
OSTI Identifier:
1009176
Report Number(s):
INL/CON-10-18347
TRN: US1101392
DOE Contract Number:
DE-AC07-05ID14517
Resource Type:
Conference
Resource Relation:
Conference: PHYSOR 2010,Pittsburgh, PA,05/09/2010,05/14/2010
Country of Publication:
United States
Language:
English
Subject:
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; ACCELERATION; CONVERGENCE; NEUTRON TRANSPORT; PHYSICS; SPHERICAL HARMONICS; TRANSPORT; VELOCITY; Acceleration; Even-Parity; Neutron Transport; Quasi-Diffusion; Second Order

Citation Formats

W. J. Martin, C. R. E. De Oliveira, and H. Park. Nonlinear Acceleration Methods for Even-Parity Neutron Transport. United States: N. p., 2010. Web.
W. J. Martin, C. R. E. De Oliveira, & H. Park. Nonlinear Acceleration Methods for Even-Parity Neutron Transport. United States.
W. J. Martin, C. R. E. De Oliveira, and H. Park. Sat . "Nonlinear Acceleration Methods for Even-Parity Neutron Transport". United States. doi:. https://www.osti.gov/servlets/purl/1009176.
@article{osti_1009176,
title = {Nonlinear Acceleration Methods for Even-Parity Neutron Transport},
author = {W. J. Martin and C. R. E. De Oliveira and H. Park},
abstractNote = {Convergence acceleration methods for even-parity transport were developed that have the potential to speed up transport calculations and provide a natural avenue for an implicitly coupled multiphysics code. An investigation was performed into the acceleration properties of the introduction of a nonlinear quasi-diffusion-like tensor in linear and nonlinear solution schemes. Using the tensor reduced matrix as a preconditioner for the conjugate gradients method proves highly efficient and effective. The results for the linear and nonlinear case serve as the basis for further research into the application in a full three-dimensional spherical-harmonics even-parity transport code. Once moved into the nonlinear solution scheme, the implicit coupling of the convergence accelerated transport method into codes for other physics can be done seamlessly, providing an efficient, fully implicitly coupled multiphysics code with high order transport.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat May 01 00:00:00 EDT 2010},
month = {Sat May 01 00:00:00 EDT 2010}
}

Conference:
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  • We have developed a highly parallel deterministic method for performing time-dependent particle (neutron, gamma-ray, or thermal radiation) transport calculations on arbitrarily connected 3-D tetrahedral meshes. The standard discrete-ordinates method, which is used to solve the first-order form of the transport equation, is extremely cumbersome to apply on such meshes and is based upon a mesh sweeping algorithm that is highly sequential in nature. A serial 1-D code for the CRAY-YMP and a parallel 1-D code for the CM-2 (Connection Machine) have been written to test our basic method. Comparisons between these two codes have shown that our new even/odd paritymore » method is highly parallelizable. 10 refs., 2 figs.« less
  • A spectral analysis is conducted for the Source Iteration (SI), and Diffusion Synthetic Acceleration (DSA) operators previously formulated for solving the Even-Parity Method (EPM) equations. In order to accommodate material heterogenity, the analysis is performed for the Periodic Horizontal Interface (PHI) configuration. The dependence of the spectral radius on the optical thickness of the two PHI layers illustrates the deterioration in the rate of convergence with increasing material discontinuity, especially when one of the layers approaches a void. The rate at which this deterioration occurs is determined for a specific material discontinuity in order to demonstrate the conditional robustness ofmore » the EPM-DSA iterations. The results of the analysis are put in perspective via numerical tests with the DANTE code (McGhee, et. al., 1997) which exhibits a deterioration in the spectral radius consistent with the theory.« less
  • A spectral analysis is conducted for the Source Iteration (SI), and Diffusion Synthetic Acceleration (DSA) operators previously formulated for solving the Even-Parity Method (EPM) equations. In order to accommodate material heterogeneity, the analysis is performed for the Periodic Horizontal Interface (PHI) configuration. The dependence of the spectral radius on the optical thickness of the two PHI layers illustrates the deterioration in the rate of convergence with increasing material discontinuity, especially when one of the layers approaches a void. The rate at which this deterioration occurs is determined for a specific material discontinuity in order to demonstrate the conditional robustness ofmore » the EPM-DSA iterations. The results of the analysis are put in perspective via numerical tests with the DANTE code (MCGhee, et al., 1997) which exhibits a deterioration in the spectral radius consitent with the theory.« less
  • No abstract prepared.