insight - Computational Complexity - # Thermal modeling of superconducting accelerator magnets using mortar thin shell approximation

Mortar Thin Shell Approximation for Efficient Thermal Analysis of Superconducting Accelerator Magnets

Q: How can the mortar TSA approach be extended to handle more complex multi-physics couplings, such as the interaction between thermal and electromagnetic effects in superconducting magnets?

The mortar TSA approach can be extended to handle complex multi-physics couplings by incorporating additional interface conditions that account for the interaction between different physical phenomena. In the context of superconducting magnets, where thermal and electromagnetic effects are crucial, the mortar TSA method can be adapted to enforce continuity not only of temperature but also of electromagnetic field quantities across the interfaces between different subdomains. To model the interaction between thermal and electromagnetic effects, the mortar TSA formulation would need to include terms that couple the heat equation with the equations governing the electromagnetic fields. This would involve introducing additional interface conditions that ensure the compatibility of the solutions for both the thermal and electromagnetic problems at the interfaces. By appropriately modifying the interface contributions and introducing suitable Lagrange multipliers, the mortar TSA method can effectively handle the coupling between thermal and electromagnetic effects in superconducting magnets.

Q: What are the potential limitations or drawbacks of the mortar TSA method compared to other techniques for modeling thin layers in finite element analysis?

While the mortar TSA method offers advantages in terms of simplifying meshing requirements for thin layers in finite element analysis, it also has some limitations and drawbacks compared to other techniques. One potential limitation is the increased complexity of implementation and computational cost associated with the mortar method. The introduction of Lagrange multipliers and additional interface conditions can lead to a more intricate formulation and solution procedure, which may require more computational resources and expertise to implement correctly. Another drawback is the need for careful consideration of the choice of basis functions and discretization strategies when using the mortar TSA method. Improper selection of basis functions or inadequate mesh refinement can lead to accuracy issues and numerical instability, especially in cases where the thin layers have complex geometries or material properties. Additionally, the mortar TSA method may struggle with handling highly nonlinear or transient phenomena in thin layers, as the coupling between different subdomains through Lagrange multipliers can introduce numerical challenges in capturing rapid changes or nonlinear behavior accurately.

Q: What insights from the thermal modeling of superconducting accelerator magnets could be applied to the design and optimization of other types of superconducting devices, such as fusion reactors or quantum computing systems?

The thermal modeling of superconducting accelerator magnets provides valuable insights that can be applied to the design and optimization of other superconducting devices, such as fusion reactors or quantum computing systems. One key insight is the importance of accurately capturing the thermal behavior of superconducting components to ensure operational safety and efficiency. By developing detailed thermal models that consider the heat generation, heat transfer mechanisms, and cooling strategies, designers can optimize the thermal management of superconducting devices to prevent overheating and maintain superconducting properties. Furthermore, the thermal modeling of superconducting accelerator magnets can inform the design of cooling systems for other superconducting devices. Understanding how different cooling methods impact the temperature distribution and overall performance of superconducting components can guide the selection of appropriate cooling techniques for fusion reactors or quantum computing systems to enhance their reliability and performance. Moreover, insights from thermal modeling can aid in the identification of potential hotspots, thermal gradients, and areas of inefficiency in superconducting devices. By optimizing the thermal design based on these insights, designers can improve the overall efficiency, longevity, and stability of superconducting systems in various applications beyond accelerator magnets.

Core Concepts

A mortar thin shell approximation method is proposed to efficiently model the thermal behavior of superconducting accelerator magnets with thin insulation layers, enabling the use of non-conforming meshes across the interfaces.

Abstract

The paper presents a mortar thin shell approximation (mortar TSA) method for the thermal analysis of superconducting accelerator magnets. Superconducting magnets often contain thin volumetric layers, such as electrical insulation or turn-to-turn contacts, which can lead to unfavorable finite element (FE) meshes.

The proposed mortar TSA approach combines the concepts of thin shell approximations (TSAs) and mortar methods to alleviate the need for conforming meshes across the thin layer interfaces. The key steps are:

The computational domain is divided into external and internal subdomains, with the thin internal layer represented by a thin shell approximation.
The internal problem is formulated using a tensor product discretization of the thin layer, leading to a 1D FE representation that avoids the need for a volumetric mesh.
Mortar methods are used to weakly couple the external and internal problems, allowing for non-conforming meshes across the interfaces.

The method is verified by comparing the results to a reference FE solution for a 2D non-linear thermal model of a simplified superconducting accelerator magnet. The mortar TSA solution shows excellent agreement with the reference, while enabling the use of independent discretizations on the two sides of the thin insulation layer.

The paper also discusses the extension of the mortar TSA approach to magnetodynamic formulations. The implementation is publicly available in the open-source finite element framework GetDP.

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Stats

The maximum temperature Tmax in the right cable of the reference solution reaches a stationary constant value over time due to the balance between the constant heat source Q and the cryogenic cooling condition.
The relative error of the mortar TSA solution compared to the reference solution is below 10^-4.

Quotes

"The mortar TSA method's formulation is derived and enables an independent discretization of the subdomains on the two sides of the TSA depending on their accuracy requirements."
"The proposed mortar TSA method enables the use of TSAs with non-conforming meshes by combining TSAs with the mortar method."

Key Insights Distilled From

Mortar Thin Shell Approximation for Analysis of Superconducting Accelerator Magnets

by Robe... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.01076.pdf

Mortar Thin Shell Approximation for Analysis of Superconducting Accelerator Magnets

Deeper Inquiries

How can the mortar TSA approach be extended to handle more complex multi-physics couplings, such as the interaction between thermal and electromagnetic effects in superconducting magnets?

The mortar TSA approach can be extended to handle complex multi-physics couplings by incorporating additional interface conditions that account for the interaction between different physical phenomena. In the context of superconducting magnets, where thermal and electromagnetic effects are crucial, the mortar TSA method can be adapted to enforce continuity not only of temperature but also of electromagnetic field quantities across the interfaces between different subdomains.
To model the interaction between thermal and electromagnetic effects, the mortar TSA formulation would need to include terms that couple the heat equation with the equations governing the electromagnetic fields. This would involve introducing additional interface conditions that ensure the compatibility of the solutions for both the thermal and electromagnetic problems at the interfaces. By appropriately modifying the interface contributions and introducing suitable Lagrange multipliers, the mortar TSA method can effectively handle the coupling between thermal and electromagnetic effects in superconducting magnets.

What are the potential limitations or drawbacks of the mortar TSA method compared to other techniques for modeling thin layers in finite element analysis?

While the mortar TSA method offers advantages in terms of simplifying meshing requirements for thin layers in finite element analysis, it also has some limitations and drawbacks compared to other techniques.
One potential limitation is the increased complexity of implementation and computational cost associated with the mortar method. The introduction of Lagrange multipliers and additional interface conditions can lead to a more intricate formulation and solution procedure, which may require more computational resources and expertise to implement correctly.
Another drawback is the need for careful consideration of the choice of basis functions and discretization strategies when using the mortar TSA method. Improper selection of basis functions or inadequate mesh refinement can lead to accuracy issues and numerical instability, especially in cases where the thin layers have complex geometries or material properties.
Additionally, the mortar TSA method may struggle with handling highly nonlinear or transient phenomena in thin layers, as the coupling between different subdomains through Lagrange multipliers can introduce numerical challenges in capturing rapid changes or nonlinear behavior accurately.

What insights from the thermal modeling of superconducting accelerator magnets could be applied to the design and optimization of other types of superconducting devices, such as fusion reactors or quantum computing systems?

The thermal modeling of superconducting accelerator magnets provides valuable insights that can be applied to the design and optimization of other superconducting devices, such as fusion reactors or quantum computing systems.
One key insight is the importance of accurately capturing the thermal behavior of superconducting components to ensure operational safety and efficiency. By developing detailed thermal models that consider the heat generation, heat transfer mechanisms, and cooling strategies, designers can optimize the thermal management of superconducting devices to prevent overheating and maintain superconducting properties.
Furthermore, the thermal modeling of superconducting accelerator magnets can inform the design of cooling systems for other superconducting devices. Understanding how different cooling methods impact the temperature distribution and overall performance of superconducting components can guide the selection of appropriate cooling techniques for fusion reactors or quantum computing systems to enhance their reliability and performance.
Moreover, insights from thermal modeling can aid in the identification of potential hotspots, thermal gradients, and areas of inefficiency in superconducting devices. By optimizing the thermal design based on these insights, designers can improve the overall efficiency, longevity, and stability of superconducting systems in various applications beyond accelerator magnets.