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Title: Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm.more » Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [3] ;  [2] ;  [4] ;  [1] ;  [2] ;  [5]
  1. Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France)
  2. (France)
  3. Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions and Institut Universitaire de France, F-75005, Paris (France)
  4. (United States)
  5. CEREMADE, Univ Paris-Dauphine, Pl. du Mal. de Lattre de Tassigny, F-75016, Paris (France)
Publication Date:
OSTI Identifier:
22382150
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 279; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; APPROXIMATIONS; BENCHMARKS; CONTROL ELEMENTS; CROSS SECTIONS; DIFFUSION; INTERPOLATION; ITERATIVE METHODS; NEUTRON DIFFUSION EQUATION; NEUTRONS; REACTOR CORES; TIME DEPENDENCE; TRANSIENTS; TRANSPORT THEORY; WATER COOLED REACTORS; WATER MODERATED REACTORS