Efficient Reduced-Order Modeling of Neutron Transport in Nuclear Reactors Using Proper Generalized Decomposition

Conceitos Básicos

Proper Generalized Decomposition (PGD) can be used to efficiently model neutron transport in nuclear reactors by separating the axial and radial dimensions, leading to reduced-order models that are computationally tractable while maintaining accuracy.

Resumo

The article presents two novel approaches for reduced-order modeling of neutron transport in nuclear reactors using Proper Generalized Decomposition (PGD):

Axial PGD: The neutron flux is separated into an expansion of radial and axial modes, allowing the axial and radial dimensions to be decoupled.
Axial-polar PGD: The neutron flux is separated into an expansion of radial and axial-polar modes, further separating the polar angle from the axial dimension.

These PGD-based reduced-order models (ROMs) can exploit the fact that nuclear reactors are typically tall but geometrically simple in the axial direction, allowing the 3D neutron flux distribution to be approximated using a low-rank "2D/1D" decomposition. The PGD approach is more general than existing 2D/1D methods, as it does not rely on simplifying assumptions about the transverse leakage.
The article derives the governing equations for the axial and axial-polar PGD ROMs, including the necessary separation of variables and Galerkin projections to obtain the 2D and 1D submodels. Additionally, it considers the alternative of assigning the energy dependence to either the radial or axial modes, or separating it out entirely, resulting in a total of six candidate 2D/1D PGD ROMs.
The performance of these PGD ROMs is assessed on two few-group benchmarks characteristic of Light Water Reactors (LWRs). The results show that both the axial and axial-polar ROMs are convergent, and the latter are often more economical than the former. The authors expect that a PGD ROM achieving a similar effect to conventional 2D/1D methods, but with superior accuracy, runtime, and broader applicability, would be highly useful, especially for full-core reactor physics problems.

Estatísticas

The article does not provide any specific numerical data or metrics to support the key claims. However, it does mention that the PGD ROMs are applied to two few-group benchmarks characteristic of Light Water Reactors, and that the results show the ROMs are convergent and the axial-polar ROMs are often more economical than the axial ROMs.

Citações

"Doing so, the radial and axial dimensions are again decoupled, notwithstanding an alternating iteration between 2D and 1D subproblems (outlined in Section 3.7). Crucially, however, this is accomplished with only a single assumption: that ψ can be adequately approximated with a tractable number of modes M."
"Ultimately, given the popularity of 2D/1D methods in reactor physics, we expect a PGD ROM which achieves a similar effect, but perhaps with superior accuracy, a quicker runtime, and/or broader applicability, would be eminently useful, especially for full-core problems."

Principais Insights Extraídos De

Reduced-order modeling of neutron transport separated in axial and radial space by Proper Generalized Decomposition with applications to nuclear reactor physics

by Kurt A. Domi... às arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18016.pdf

Perguntas Mais Profundas

How can the performance and accuracy of the PGD-based ROMs be further improved, especially for more complex reactor geometries and operating conditions?

To enhance the performance and accuracy of PGD-based Reduced-Order Models (ROMs) for complex reactor geometries and operating conditions, several strategies can be implemented:

Increased Model Order: By increasing the number of modes (M) used in the PGD decomposition, a more accurate representation of the neutron flux distribution can be achieved. This allows for a finer approximation of the 3D solution and can lead to improved accuracy, especially in regions with significant flux gradients.

Adaptive Enrichment: Implementing adaptive enrichment techniques can dynamically adjust the number of modes based on the complexity of the problem. This adaptive approach ensures that computational resources are focused where they are most needed, optimizing the balance between accuracy and computational cost.

Incorporating Physics-Informed Constraints: By incorporating physics-informed constraints into the PGD framework, such as boundary conditions and material properties, the ROMs can better capture the underlying physics of the neutron transport problem. This can lead to more accurate results, especially in scenarios with intricate geometries and material compositions.

Integration of Machine Learning: Utilizing machine learning algorithms in conjunction with PGD can help in capturing complex patterns and relationships within the data. This hybrid approach can improve the predictive capabilities of the ROMs, especially in scenarios where traditional methods may struggle to capture all nuances.

Verification and Validation: Rigorous verification and validation procedures should be employed to ensure the accuracy and reliability of the PGD-based ROMs. Comparing the results with high-fidelity simulations and experimental data can help identify areas for improvement and enhance the overall performance of the models.

What are the potential limitations or drawbacks of the PGD approach compared to other reduced-order modeling techniques, such as Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD)?

While Proper Generalized Decomposition (PGD) offers several advantages, it also has some limitations and drawbacks compared to other reduced-order modeling techniques like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD):

Computational Complexity: PGD can be computationally intensive, especially when dealing with high-dimensional problems or large datasets. The iterative nature of PGD may require more computational resources compared to some other reduced-order modeling techniques.

Convergence Issues: Convergence of PGD-based ROMs can be challenging, particularly in scenarios with complex geometries or highly nonlinear behavior. Ensuring convergence and stability of the models may require careful tuning of parameters and regularization techniques.

Interpretability: PGD models may be less interpretable compared to some other techniques like POD, which provide clear physical insight into the dominant modes of the system. Understanding the underlying physics of the problem based on the PGD results can be more challenging.

Limited Applicability: PGD may not be as widely applicable to diverse problems as some other reduced-order modeling techniques. Its effectiveness can vary depending on the specific characteristics of the problem, and it may not always be the best choice for certain scenarios.

Data Requirements: PGD may require a significant amount of training data to accurately capture the system dynamics. In cases where data availability is limited, other techniques like POD or DMD, which are more data-efficient, may be preferred.

How can the PGD-based ROMs be integrated with existing reactor physics simulation tools and workflows to enable their practical adoption in the nuclear industry?

Integrating PGD-based Reduced-Order Models (ROMs) with existing reactor physics simulation tools and workflows can facilitate their practical adoption in the nuclear industry. Here are some steps to enable this integration:

Compatibility and Interoperability: Ensure that the PGD-based ROMs are compatible with the input/output formats and data structures used in existing reactor physics simulation tools. This includes compatibility with standard file formats, data exchange protocols, and simulation codes.

API Development: Develop Application Programming Interfaces (APIs) that allow seamless communication between the PGD-based ROMs and existing simulation tools. This enables data transfer, parameter setting, and result retrieval between the different components.

Validation and Benchmarking: Validate the PGD-based ROMs against existing high-fidelity simulations and benchmark problems commonly used in the nuclear industry. Demonstrating the accuracy and reliability of the ROMs is essential for their acceptance and adoption.

Training and Support: Provide training and support to users of the integrated system to ensure they understand how to effectively utilize the PGD-based ROMs within the existing simulation workflows. This includes documentation, tutorials, and user guides.

Incremental Implementation: Gradually introduce the PGD-based ROMs into the existing workflow, starting with pilot projects or specific use cases. This incremental approach allows for testing, feedback incorporation, and gradual adoption across different applications.

Performance Optimization: Optimize the performance of the integrated system by leveraging parallel computing, efficient algorithms, and hardware acceleration where applicable. This ensures that the ROMs can be seamlessly integrated without compromising computational efficiency.

By following these steps and considerations, the PGD-based ROMs can be effectively integrated into existing reactor physics simulation tools and workflows, enabling their practical adoption and utilization in the nuclear industry.