The Analytic Coarse-Mesh Finite Difference Method for Multigroup and Multidimensional Diffusion Calculations

Aragonés Beltrán, José María and Ahnert Iglesias, Carolina and García Herranz, Nuria (2007). The Analytic Coarse-Mesh Finite Difference Method for Multigroup and Multidimensional Diffusion Calculations. "Nuclear Science and Engineering", v. 157 (n. 1); pp. 1-15. ISSN 0029-5639.

Description

Title: The Analytic Coarse-Mesh Finite Difference Method for Multigroup and Multidimensional Diffusion Calculations
Author/s:
  • Aragonés Beltrán, José María
  • Ahnert Iglesias, Carolina
  • García Herranz, Nuria
Item Type: Article
Título de Revista/Publicación: Nuclear Science and Engineering
Date: September 2007
Volume: 157
Subjects:
Faculty: E.T.S.I. Industriales (UPM)
Department: Ingeniería Nuclear [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this work we develop and demonstrate the analytic coarse-mesh finite difference (ACMFD) method for multigroup - with any number of groups - and multidimensional diffusion calculations of eigenvalue and external source problems. The first step in this method is to reduce the coupled system of the G multigroup diffusion equations, inside any homogenized region (or node) of any size, to the G independent modal equations in the real or complex eigenspace of the G × G multigroup matrix. The mathematical and numerical analysis of this step is discussed for several reactor media and number of groups. As a second step, we discuss the analytical solutions in the general (complex) modal eigenspace for one-dimensional plane geometry, deriving the generalized Chao's relation among the surface fluxes and the net currents, at a given interface, and the node-average fluxes, essential in the ACMFD method. We also introduce here the treatment of heterogeneous nodes, through modal interface flux discontinuity factors, and show the analytical and numerical application to core-reflector problems, for a single infinite reflector and for reflectors with two layers of different materials. Then, we address the general multidimensional case, with rectangular X-Y-Z geometry considered, showing the equivalency of the methods of transverse integration and incomplete expansion of the multidimensional fluxes, in the real or complex modal eigenspace of the multigroup matrix. A nonlinear iteration scheme is implemented to solve the multigroup multidimensional nodal problem, which has shown a fast and robust convergence in proof-of-principle numerical applications to realistic pressurized water reactor cores, with heterogeneous fuel assemblies and reflectors.

Funding Projects

TypeCodeAcronymLeaderTitle
Unspecified516560 (FI60)NURESIMUnspecifiedSixth EURATOM Framework - ProgrammeIntegrated Project NURESIM “European Platform for Nuclear Reactor Simulations2
UnspecifiedENE2005-020640 FTNUnspecifiedMinisterio de Ciencia y TecnologíaUnspecified

More information

Item ID: 44292
DC Identifier: http://oa.upm.es/44292/
OAI Identifier: oai:oa.upm.es:44292
Official URL: http://www.ans.org/store/article-2709/
Deposited by: Memoria Investigacion
Deposited on: 10 Jan 2017 08:38
Last Modified: 12 Jan 2017 11:33
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