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Title: A new mathematical adjoint for the modified SAAF-SN equations

We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF-SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF-SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF-SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.
Authors:
 [1] ;  [1] ;  [1] ;  [1]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
OSTI Identifier:
1162217
Report Number(s):
INL/JOU--14-32514
Journal ID: ISSN 0306-4549; TRN: US1500179
DOE Contract Number:
AC07-05ID14517
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 75; Journal Issue: C
Publisher:
Elsevier
Research Org:
Idaho National Laboratory (INL), Idaho Falls, ID (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 22 GENERAL STUDIES OF NUCLEAR REACTORS; EQUATIONS; SOLUTIONS; EIGENVALUES; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; IMPLEMENTATION; SIMULATION; STABILIZATION; ADJOINT FLUX; FINITE ELEMENT METHOD; NEUTRON TRANSPORT THEORY Adjoint; Linear Transport Equation; SAAF-SN equations