An a posteriori residual-based spatial discretization error estimator for SN neutron transport

Hart, Nathan H.; Azmy, Yousry Y.; Duo, Jose I.

doi:10.1016/j.anucene.2019.107092

An a posteriori residual-based spatial discretization error estimator for S_N neutron transport

Journal Article · Tue Nov 05 23:00:00 EST 2019 · Annals of Nuclear Energy (Oxford)

DOI:https://doi.org/10.1016/j.anucene.2019.107092· OSTI ID:1801121

Hart, Nathan H. ^[1]; Azmy, Yousry Y. ^[2]; Duo, Jose I. ^[3]

North Carolina State Univ., Raleigh, NC (United States); OSTI
North Carolina State Univ., Raleigh, NC (United States)
IMPSA Argentina, Mendoza (Argentina)

The “residual source estimator”, an implicit residual-based spatial discretization error estimator for S_N neutron transport methods, is introduced. The estimator uses an approximation of the residual as a fixed source for an analogous transport problem whose solution is the error estimate, using the same transport operator as the original numerical solution. The complete derivation of the residual source estimator, the approximation of the residual, and higher-order derivatives is included. The performance of the residual source estimator for 0-order DGFEM is tested against reference solutions. For problems with true solutions discontinuous in the first derivative across the singular characteristics, the residual source estimator is generally accurate, precise, and computationally affordable compared to similar estimators. It suffers in problems where solutions are discontinuous, particularly when the discontinuity inflicts significant inaccuracies on the discrete solution; however, compared to other estimators, which suffer similarly, it remains a competitive option.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Nuclear Energy (NE)

Grant/Contract Number:: NA0002576

OSTI ID:: 1801121

Alternate ID(s):: OSTI ID: 2325053

Journal Information:: Annals of Nuclear Energy (Oxford), Journal Name: Annals of Nuclear Energy (Oxford) Vol. 137; ISSN 0306-4549

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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discretization
error estimation
finite elements
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residual

An a posteriori residual-based spatial discretization error estimator for SN neutron transport

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An a posteriori residual-based spatial discretization error estimator for S_N neutron transport