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Reduced Basis Approaches in Time-Dependent Non-Coercive Settings for Modelling the Movement of Nuclear Reactor Control Rods

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Numerical methods in calculus of variations and optimal control Computer aspects of numerical algorithms

Published online by Cambridge University Press:  22 June 2016

Alberto Sartori ,
Antonio Cammi ,
Lelio Luzzi  and
Gianluigi Rozza
Alberto Sartori*
Affiliation:
Politecnico di Milano – Department of Energy, CeSNEF, Enrico Fermi Center for Nuclear Studies, via La Masa 34, 20156 Milano, Italy SISSA, International School for Advanced Studies, Mathematics Area – mathLab, Via Bonomea 265, 34136 Trieste, Italy
Antonio Cammi*
Affiliation:
Politecnico di Milano – Department of Energy, CeSNEF, Enrico Fermi Center for Nuclear Studies, via La Masa 34, 20156 Milano, Italy
Lelio Luzzi*
Affiliation:
Politecnico di Milano – Department of Energy, CeSNEF, Enrico Fermi Center for Nuclear Studies, via La Masa 34, 20156 Milano, Italy
Gianluigi Rozza*
Affiliation:
SISSA, International School for Advanced Studies, Mathematics Area – mathLab, Via Bonomea 265, 34136 Trieste, Italy
*
*Corresponding author. Email addresses:[email protected] (A. Sartori), [email protected] (A. Cammi), [email protected] (L. Luzzi), [email protected] (G. Rozza)
*Corresponding author. Email addresses:[email protected] (A. Sartori), [email protected] (A. Cammi), [email protected] (L. Luzzi), [email protected] (G. Rozza)
*Corresponding author. Email addresses:[email protected] (A. Sartori), [email protected] (A. Cammi), [email protected] (L. Luzzi), [email protected] (G. Rozza)
*Corresponding author. Email addresses:[email protected] (A. Sartori), [email protected] (A. Cammi), [email protected] (L. Luzzi), [email protected] (G. Rozza)
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Abstract

In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

Keywords

Reduced basis methodcontrol rod movementspatial kineticsparametrized geometrymulti-group neutron diffusionnon-coercive operators

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65Y20: Complexity and performance of numerical algorithms 49M25: Discrete approximations
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 1 , July 2016 , pp. 23 - 59
Copyright
Copyright © Global-Science Press 2016 

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