Finite-Element Formulations for Systems With High-Temperature Superconductors

• Published in: IEEE transactions on applied superconductivity Vol. 30; no. 3; pp. 1 - 13
• Main Authors: Dular, Julien, Geuzaine, Christophe, Vanderheyden, Benoit
• Format: Journal Article Web Resource
• Language: English
• Published: New York IEEE 01.04.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Concavity; Convexity; Electrical & electronics engineering; Engineering, computing & technology; Ferromagnetic materials; Finite element method; Finite-element (FE) analysis; Finite-Element Analysis; Formulations; High temperature superconductors; high-temperature superconductors (HTSs); Ingénierie électrique & électronique; Ingénierie, informatique & technologie; Iron; Iterative methods; Magnetic flux; Magnetic levitation; magnetic materials; Magnetic noise; Magnetic shielding; Mathematical analysis; Nonlinear Equations; Saturation magnetization; Superconducting magnets
• ISSN: 1051-8223; 1558-2515; 1558-2515
• DOI: 10.1109/TASC.2019.2935429

In this article, we consider finite-element models for high-temperature superconductors and compare two dual formulations, either magnetic-field conforming or magnetic-flux-density conforming. The electrical resistivity of superconductors is described by a power law and is strongly nonlinear. We compare the accuracy and the efficiency of the dual formulations by starting from simple considerations on the concavity/convexity of the constitutive law involved in each case. We then study the numerical behavior of each formulation in one-, two-, and three-dimensional problems and compare their results against benchmarks. We draw general recommendations for the choice of a formulation, an iteration scheme for treating the corresponding linearized constitutive law, and a time-stepping extrapolation scheme. This approach is extended to soft ferromagnetic materials with a saturation law. Since the outcome of our analysis shows that recommended formulations for treating ferromagnets are just the opposite of those for treating superconductors, we suggest a coupled formulation for systems where both types of materials are present. The coupled formulation is shown to be accurate and more efficient than single formulations applied indistinctly to all materials.