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    Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

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    Type
    Article
    Authors
    Wang, Yaqi
    Bangerth, Wolfgang
    Ragusa, Jean
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2009-04
    Permanent link to this record
    http://hdl.handle.net/10754/600016
    
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    Abstract
    Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made efficient by deriving all meshes from a common coarse mesh by hierarchic refinement. Our methods are formulated using conforming finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library's extensively documented tutorial. We illustrate our methods with results for 2-D and 3-D reactor simulations using 2 and 7 energy groups, and using conforming finite elements of polynomial degree up to 6. © 2008 Elsevier Ltd. All rights reserved.
    Citation
    Wang Y, Bangerth W, Ragusa J (2009) Three-dimensional h-adaptivity for the multigroup neutron diffusion equations. Progress in Nuclear Energy 51: 543–555. Available: http://dx.doi.org/10.1016/j.pnucene.2008.11.005.
    Sponsors
    Part of this research was funded through DOE grants DE-FG07-071D14767 and DE-FG07-051D74692. This publication is also partly based on work supported by Award No. KUS-C1-016-04, made by the King Abdullah University of Science and Technology (KAUST).
    Publisher
    Elsevier BV
    Journal
    Progress in Nuclear Energy
    DOI
    10.1016/j.pnucene.2008.11.005
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.pnucene.2008.11.005
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