Development of a three-dimensional finite-element model for high-temperature superconductors based on the H-formulation

Finite-element models are a powerful and widely used tool for evaluating the ac losses of HTS tapes and wires as well as of assemblies such as cables and coils. The H-formulation, which uses the magnetic field components as state variables, has proved to be an efficient implementation to solve 2-D problems, involving infinitely long or axially-symmetric geometries; an excellent agreement with experimental data has been found in many cases. However, the simulation of certain applications requires a full 3-D model. In this paper we report on the development of a 3-D model based on the H-formulation. We describe the implementation of Maxwell equations, the imposition of current constraints and we discuss the issues related to meshing 3-D volumes. The model is validated by comparing the results with those obtained with 2-D models in cases that can be investigated in 2-D; then, it is used to simulate cases that can be handled only in 3-D.

► We successfully implemented a 3-D model for time-dependent simulations of HTS using the H-formulation.
► The model has been validated by comparing the results with cases that can be solved in 2-D.
► The model has been used to show different examples of application on 3-D geometries.
► The model can be used to study very interesting cases for practical applications.
► The choice of an appropriate mesh is of paramount importance.