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Mortar Thin Shell Approximation for Analysis of Superconducting Accelerator Magnets

Robert Hahn, Erik Schnaubelt, Mariusz Wozniak, Christophe Geuzaine, Sebastian Schöps

Abstract

Thin layers can lead to unfavorable meshes in a finite element (FE) analysis. Thin shell approximations (TSAs) avoid this issue by removing the need for a mesh of the thin layer while approximating the physics across the layer by an interface condition. Typically, a TSA requires the mesh of both sides of the TSA interface to be conforming. To alleviate this requirement, we propose to combine mortar methods and TSAs for solving the heat equation. 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 method is verified by comparison with a reference FE solution of a thermal model problem of a simplified superconducting accelerator magnet.

Mortar Thin Shell Approximation for Analysis of Superconducting Accelerator Magnets

Abstract

Thin layers can lead to unfavorable meshes in a finite element (FE) analysis. Thin shell approximations (TSAs) avoid this issue by removing the need for a mesh of the thin layer while approximating the physics across the layer by an interface condition. Typically, a TSA requires the mesh of both sides of the TSA interface to be conforming. To alleviate this requirement, we propose to combine mortar methods and TSAs for solving the heat equation. 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 method is verified by comparison with a reference FE solution of a thermal model problem of a simplified superconducting accelerator magnet.
Paper Structure (6 sections, 14 equations, 4 figures)

This paper contains 6 sections, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Classical Weak Formulation
  3. Mortar Thin Shell Formulation
  4. Numerical Example
  5. Conclusion
  6. Acknowledgement

Figures (4)

  • Figure 1: Cross-section of computational domain $\Omega$ for the meshed reference (left) and mortar TSA (right), which also shows a sketch of a non-conforming mesh. The reference mesh is omitted for the sake of a clear visualization.
  • Figure 2: Tensor product discretization of $\hat{\Omega}_\mathrm{i}$.
  • Figure 3: Maximum temperature $T_\mathrm{max}$ in the right cable. Reference solution and relative error over time.
  • Figure 4: Simplified accelerator magnet model with temperature-dependent material properties (not to scale). Blue lines designate mortar TSA insulation layers. The model heats up over time due to the heat source in the cables.