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Title: Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation

Abstract

Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.

Authors:
; ;
Publication Date:
Research Org.:
Idaho National Laboratory (INL)
Sponsoring Org.:
USDOE
OSTI Identifier:
1120821
Report Number(s):
INL/JOU-14-31308
Journal ID: ISSN 0029-5639
DOE Contract Number:  
DE-AC07-05ID14517
Resource Type:
Journal Article
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 175; Journal Issue: 3; Journal ID: ISSN 0029-5639
Publisher:
American Nuclear Society
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; angular flux form

Citation Formats

Sanchez, Richard, Rabiti, Cristian, and Wang, Yaqi. Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation. United States: N. p., 2012. Web. doi:10.13182/NSE12-50.
Sanchez, Richard, Rabiti, Cristian, & Wang, Yaqi. Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation. United States. doi:10.13182/NSE12-50.
Sanchez, Richard, Rabiti, Cristian, and Wang, Yaqi. Thu . "Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation". United States. doi:10.13182/NSE12-50.
@article{osti_1120821,
title = {Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation},
author = {Sanchez, Richard and Rabiti, Cristian and Wang, Yaqi},
abstractNote = {Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.},
doi = {10.13182/NSE12-50},
journal = {Nuclear Science and Engineering},
issn = {0029-5639},
number = 3,
volume = 175,
place = {United States},
year = {2012},
month = {11}
}