Efficient modeling of high temperature superconductors surrounded by magnetic components using a reduced H-$\phi$ formulation

TL;DR

This paper introduces an efficient H-$$ formulation for modeling high-temperature superconductors with magnetic components, significantly reducing computation time while maintaining accuracy in complex simulations.

Contribution

It presents a novel H-$$ formulation that separates source and reaction fields, improving efficiency over traditional methods in superconductor-magnet interaction modeling.

Findings

Computation times reduced by nearly three and four times in 2-D and 3-D simulations.

The H-$$ formulation achieves excellent agreement with the H-formulation.

It is more accurate and efficient than the H-A formulation in 2-D simulations.

Abstract

Although the H-formulation has proven to be one of the most versatile formulations used to accurately model superconductors in the finite element method, the use of vector dependent variables in non-conducting regions leads to unnecessarily long computation times. Additionally, in some applications of interest, the combination of multiple magnetic components interacting with superconducting bulks and/or tapes leads to large domains of simulation. In this work, we separate the magnetic field into a source and reaction field and use the H-$\phi$ formulation to efficiently simulate a superconductor surrounded by magnetic bodies. We model a superconducting cube between a pair of Helmholtz coils and a permanent magnet levitating above a superconducting pellet. In both cases, we find excellent agreement with the H-formulation, while the computation times are reduced by factors of nearly three and four in 2-D and 3-D, respectively. Finally, we show that the H-$\phi$ formulation is more accurate and efficient than the H-A formulation in 2-D.