期刊
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
卷 30, 期 3, 页码 -出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TASC.2019.2935429
关键词
Finite-element (FE) analysis; high-temperature superconductors (HTSs); magnetic materials; nonlinear equations
资金
- Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) [2.5020.11]
- F.R.S-FNRS
- Consortium des Equipements de Calcul Intensif (CECI)
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.
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