Conclusion

The work done during this internship is a first step to create an activity of High critical Temperature Superconductors modeling with formulations that are adapted to different types of problems. It gave a deep knowledge of the methods of simulations and modeling of multiphysics nonlinear problems that define the HTS superconducting magnets. This allowed me to understand the challenges and difficulties surrounding the development of such models. I also actively looked for solutions to implement them with free software, less universally used, but which have the advantage of being free of charge as well as a greater freedom of control over the modeling.

1. My work

During this internship, I have implemented several formulations on multiple software to model HTS :

  • A-Formulation in axisymmetric and 2D coordinates for Superconductors on Feelpp CFPDES, getDP, FreeFEM & Comsol

  • H-Formulation in axisymmetric coordinates for Superconductors on getDP & Comsol

  • T-A-Formulation in axisymmetric coordinates for Superconductors on Feelpp CFPDES, getDP & Comsol

I also contributed to the development of the application Python MagnetSetup and added missing formulations on it, as well as developing a python "bridge" between Feelpp CFPDES models and Comsol.

2. Next Steps

The next steps after this work would to start studying the HTS models coupled to the thermal physic, because the superconductors highly depends on the temperature. Also, the implementations of the HTS already made need to be adapted to the superconducting magnets of the LNCMI, to start an HTS modeling activity in addition to the experimental activity. Finally, we need to start implementing the formulations on 3D geometries, using the saddle-point or the regularized A formulation for example.

2.1. Missing features for Feelpp CFPDEs:

The use of feelpp is a priority compared to the other software, but some features are still missing to be able to model all formulations. Among these are :

  • The coupling of formulations on edges (for the different coupled magnetic formulations)

  • The surface Lagrange multipliers (for transport current problems)

  • The possibility to solve 1D PDE (for the T-A Formulation without the homogeneous approximation)

3. Acknowledgments

I would like to thank my supervisor Chirstophe Trophime for his help and presence during this internship, as well as the team of the U building of the LNMCI for welcoming me in the laboratory. I would also like to thank Christophe Prud’homme, Vincent Chabannes and all the Cemosis team for their help and answer to all my Feelpp related questions and other interrogations.