A combined immersed body and adaptive mesh method for simulating neutron transport within complex structures

Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.

doi:10.1016/j.anucene.2019.05.044

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…It can be seen that the basis functions identified discontinuities that will have been present in the snapshots. The next stage is to project the matrices of the high-fidelity model for each set of parameters onto the POD basis functions, and for 10 layers, this results in 1240 matrices: [1,10]. We are now in a position to run the reduced-order model.…”

Section: Global Proper Orthogonal Decompositionmentioning

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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Section: Global Proper Orthogonal Decompositionmentioning

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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“…Although, in many areas, adding diffusion or solving diffusion problems often leads to fields that are smooth and well able to be represented accurately with POD basis functions, in other areas, such as reactor physics, one is often confronted by problems with abruptly changing fields similar to advection problems. A good example is a control rod that is partially inserted into a reactor, where one would see a near zero flux within the control rod and a much higher flux a small distance away from the control rod; see the scalar flux solutions shown in Buchan et al 52 for instance. This similarity between advection and diffusion problems is also seen in discretization methods such as the self‐adjoint angular flux method, 53 in which the first‐order transport equations are transformed into a series of diffusion‐like equations with the application of a least squares principle and a particular weighting.…”

Section: Introductionmentioning

confidence: 99%

An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion

Phillips

Heaney

Smith

et al. 2021

Numerical Meth Engineering

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Using an autoencoder for dimensionality reduction, this article presents a novel projection-based reduced-order model for eigenvalue problems.Reduced-order modeling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.

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“…Although, in many areas, adding diffusion or solving diffusion problems often leads to fields that are smooth and well able to be represented accurately with POD basis functions, in other areas, such as reactor physics, one is often confronted by problems with abruptly changing fields similar to advection problems. A good example is a control rod that is partially inserted into a reactor, where one would see a near zero flux within the control rod and a much higher flux a small distance away from the control rod; see the scalar flux solutions shown in Buchan et al [9] for instance. This similarity between advection and diffusion problems is also seen in discretisation methods such as the Self Adjoint Angular Flux method [40], in which the first order transport equations are transformed into a series of diffusion-like equations with the application of a least squares principle and a particular weighting.…”

Section: Introductionmentioning

confidence: 99%

An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

Phillips¹,

Heaney²,

Smith³

et al. 2020

Preprint

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Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results.Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.

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A combined immersed body and adaptive mesh method for simulating neutron transport within complex structures

Cited by 4 publications

References 31 publications

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

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

An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion

An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

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