Thin-Shell Approach for Modeling Superconducting Tapes in the $H$-$\phi$ Finite-Element Formulation

TL;DR

This paper introduces a thin-shell finite-element method combined with the $H$-$$ formulation to efficiently model superconducting tapes, reducing computational costs while maintaining accuracy for complex electromagnetic simulations.

Contribution

The paper presents a novel thin-shell approach integrated with the $H$-$$ formulation, enabling efficient and accurate modeling of superconducting tapes with complex geometries.

Findings

Good agreement with reference solutions in magnetic field profiles.

The method reduces computational cost compared to traditional models.

Increasing auxiliary FE elements improves accuracy at small inter-tape distances.

Abstract

This paper presents a novel finite-element approach for the electromagnetic modeling of superconducting coated conductors. We combine a thin-shell (TS) method to the $H$-$\phi$ formulation to avoid the meshing difficulties related to the high aspect ratio of these conductors and reduce the computational burden in simulations. The interface boundary conditions in the TS method are defined using an auxiliary 1-D finite-element (FE) discretization of $N$ elements along the thinnest dimension of the conductor. This procedure permits the approximation of the superconductor's nonlinearities inside the TS in a time-transient analysis. Four application examples of increasing complexity are discussed: (i) single coated conductor, (ii) two closely packed conductors carrying anti-parallel currents, (iii) a stack of twenty superconducting tapes and a (iv) full representation of a HTS tape comprising a stack of thin films. In all these examples, the profiles of both the tangential and normal components of the magnetic field show good agreement with a reference solution obtained with standard $2$-D $H$-$\phi$ formulation. Results are also compared with the widely used $T$-$A$ formulation. This formulation is shown to be dual to the TS model with a single FE ($N=1$) in the auxiliary 1-D systems. The increase of $N$ in the TS model is shown to be advantageous at small inter-tape separation and low transport current since it allows the tangential components of the magnetic field to penetrate the thin region. The reduction in computational cost without compromising accuracy makes the proposed model promising for the simulation of large-scale superconducting applications.