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Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale

Abstract

The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally,  More>>
Authors:
Publication Date:
Jul 01, 2001
Product Type:
Technical Report
Report Number:
CEA-R-5959
Resource Relation:
Other Information: 79 refs; PBD: 2001
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; BOLTZMANN EQUATION; CONFORMAL MAPPING; FINITE ELEMENT METHOD; HEXAGONAL CONFIGURATION; MESH GENERATION; NEUTRON DIFFUSION EQUATION; NEUTRON TRANSPORT THEORY; PWR TYPE REACTORS
OSTI ID:
20241530
Research Organizations:
CEA Saclay, Dept. de Modelisation des Systemes et Structures, 91 - Gif sur Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR0200065015082
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
189 pages
Announcement Date:
Apr 30, 2002

Citation Formats

Schneider, D. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale. France: N. p., 2001. Web.
Schneider, D. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale. France.
Schneider, D. 2001. "Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale." France.
@misc{etde_20241530,
title = {Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry; Elements finis mixtes duaux pour la resolution numerique de l'equation de la diffusion neutronique en geometrie hexagonale}
author = {Schneider, D}
abstractNote = {The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)}
place = {France}
year = {2001}
month = {Jul}
}