An Adjoint Proper Orthogonal Decomposition method for a neutronics reduced order model

Lorenzi, Stefano

doi:10.1016/j.anucene.2017.12.029

Cited by 16 publications

(9 citation statements)

References 29 publications

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“…Indeed, POD was introduced to study the coherent structures in experimental turbulent flows. In the nuclear field (as in other fields of engineering), it has been shown that POD basis functions carry out physical information on distribution of scalar and energy group fluxes, fluid velocity distributions in thermal-hydraulics and cross section uncertainties [21][22][23][24]. For this reason, we expect that POD modes for burnup matrices and fluxes provide the main physical information on fuel burnup.…”

Section: Motivation Of the Methodologymentioning

confidence: 96%

“…We compare ROM and FOM results for reactivity and nuclide concentrations over time. Indeed, FOM against ROM is the standard procedure employed in the evaluation of the quality of the approximation in ROM [21,24]. Nevertheless, it should be noted that comparisons with experimental data and other approaches for burnup analysis, such as those developed for neutronics deterministic solvers, are mandatory for the assessment of the methodology.…”

Section: Physics Area Model Assumptionmentioning

confidence: 99%

“…In the nuclear field, POD has been successfully applied to neutronics [21][22][23], thermal-hydraulics [24], sensitivity and uncertainty quantification [25,26]. Notwithstanding, there is a lack of literature in the employment in burnup calculations, nevertheless it would be necessary to solve the issue of computational burden previously discussed.…”

Section: Introductionmentioning

confidence: 99%

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Development of a Reduced Order Model for Fuel Burnup Analysis

Castagna

Aufiero²,

Lorenzi

et al. 2020

Energies

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Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

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Section: Motivation Of the Methodologymentioning

confidence: 96%

Section: Physics Area Model Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of a Reduced Order Model for Fuel Burnup Analysis

Castagna

Aufiero²,

Lorenzi

et al. 2020

Energies

Self Cite

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“…For brevity of the exposition, the reduced basis will always be sought through a POD decomposition and the reduced system will always be obtained using Galerkin projection. We refer the reader to [38,39] for other reduced basis approaches and to [40] for Petrov-Galerkin projection-based ROM.…”

Section: Model Order Reduction: Backgroundmentioning

confidence: 99%

Application of multiphysics model order reduction to doppler/neutronic feedback

German

Ragusa

Fiorina

2019

EPJ Nuclear Sci. Technol.

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In this paper, a proper orthogonal decomposition based reduced-order model is presented for parametrized multiphysics computations. Our application physics is Doppler feedback in a simplified model of the molten salt fast reactor concept. The reduced model is created using the method of snapshots where the offline training set is obtained by exercising a full-order model created with the OpenFOAM based multiphysics solver, GeN-Foam. The steady state models solve the multi-group diffusion k-eigenvalue equations with moving precursors together with the energy equation. A fixed velocity field is assumed throughout the computations, hence the momentum and continuity equations are not solved. The discrete empirical interpolation method is used for the efficient coupling of the ROM solvers, while the input parameter space is surveyed using the improved distributed latin hypercube sampling algorithm.

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“…This work was later built upon in [17] to model the movement of control rods. Lorenzi [18] showed that POD can be combined using an adjoint flux, where basis functions are produced from both the flux and adjoint flux snapshots, to produce solutions that are more accurate than only using standard POD. All these ROMs show computational gains of at least three orders of magnitude over the HFMs.…”

Section: Introductionmentioning

confidence: 99%

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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An Adjoint Proper Orthogonal Decomposition method for a neutronics reduced order model

Cited by 16 publications

References 29 publications

Development of a Reduced Order Model for Fuel Burnup Analysis

Development of a Reduced Order Model for Fuel Burnup Analysis

Application of multiphysics model order reduction to doppler/neutronic feedback

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

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