A reduced-basis element method for pin-by-pin reactor core calculations in diffusion and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">SP</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>approximations

Cherezov, Alexey; Sanchez, Richard; Joo, Han Gyu

doi:10.1016/j.anucene.2018.02.013

Cited by 18 publications

(9 citation statements)

References 12 publications

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“…Instead, we form local solutions, obtain POD basis functions based on these solutions, which are then used to form the ROM across the whole reactor. The results also demonstrate that constructing basis functions from clusters (i.e., groups of sub-domains), as done by Cherezov et al [26], produces solutions that are almost as good as using solutions from the entire domain. Section 2 describes the methodology including the governing equations, discretisation, reduced-order modelling methods, domain decomposition methods, the test case and how the different ROMs are constructed.…”

Section: Introductionmentioning

confidence: 58%

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Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

et al. 2021

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Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

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Section: Introductionmentioning

confidence: 58%

“…An application to neutron transport was provided by Cherezov et al [26]. Here, a non-overlapping domain decomposition method was combined with POD and applied to a full reactor core, which was decomposed into sub-domains containing fuel assemblies.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

et al. 2021

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“…For discretising the neutron diffusion equation, the most commonly used methods are the finite difference method, the finite element method, and nodal methods [40][41][42]. The latter give fast and accurate solutions, but require a reconstruction step to obtain the pin-power distribution [37]. Using finite element or finite difference methods avoids this step.…”

Section: Discretisation Of the High-fidelity Modelmentioning

confidence: 99%

“…The computational domains lend themselves to decomposition into physically meaningful subdomains, as, for example, a reactor consists of many fuel assemblies and an assembly comprises many fuel pins. Jamelot and Ciarlet Jr [36] and Cherezov et al [37] both applied these methods to neutron diffusion, the latter applying a reduced basis method to subsets or clusters of assemblies making up a simple reactor with promising results. Phillips et al [38] proposed several methods combining domain decomposition and ROMs, in which the basis functions are derived by grouping together snapshots relating to (i) the same material type, (ii) the same location (sub-domain), (iii) the same material type and location.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

et al. 2021

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Producing high-fidelity real-time simulations of neutron diffusion in a reactor is computationally extremely challenging, due, in part, to multiscale behaviour in energy and space. In many scientific fields, including nuclear modelling, the application of reduced-order modelling can lead to much faster computation times without much loss of accuracy, paving the way for real-time simulation as well as multi-query problems such as uncertainty quantification and data assimilation. This paper compares two reduced-order models that are applied to model the movement of control rods in a fuel assembly for a given temperature profile. The first is a standard approach using proper orthogonal decomposition (POD) to generate global basis functions, and the second, a new method, uses POD but produces global basis functions that are local in the parameter space (associated with the control-rod height). To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height. This is seen to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for keff and by one order of magnitude for the scalar flux.

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“…These techniques have seen extensive use in the fluid dynamics community for the modeling of general nonlinear flows [19,20], linearized flows [21], compressible flows [22], turbulence [23,11] and other applications [24,25]. Naturally the same techniques also have a wide range of applicability in the development of ROMs for particle transport, and have been used to model linear particle transport problems [26,27,28,29,30,31], neutron transport in reactor-physics problems [32,33,34], and nonlinear radiative transfer [35,36,37,38,39].…”

Section: Introductionmentioning

confidence: 99%

Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor

Coale¹,

Anistratov²

2021

Preprint

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A new group of reduced-order models (ROMs) for nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. The Eddington (quasidiffusion) tensor that provides exact closure for the system of moment equations is approximated via one of several data-based methods of model-order reduction. These methods are the (i) proper orthogonal decomposition, (ii) dynamic mode decomposition (DMD), (iii) an equilibrium-subtracted DMD variant. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be accurate even with very low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

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A reduced-basis element method for pin-by-pin reactor core calculations in diffusion andSP3approximations

Cited by 18 publications

References 12 publications

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor

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