New Hybrid FE-FV Method for Computing Current Distribution in 2-D Superconductors: Application to an HTS Cylinder in Transverse Magnetic Field

This paper presents a new numerical method based on finite elements - finite volumes (FE-FV) for solving 2-D diffusion problems in high temperature superconductors (HTS). The approach does not involve directly the resistivity term (rho), generally used to model the E(J) characteristic as a power law, i.e E(J) = rho(J)J, with rho(J) prop J ^n-1. Instead, we use a J(E) constitutive law J prop E ^(1/n), with E ^rarr = Ee ^rarr _z (a single component), which leads to a scalar non-linear differential equation. After presenting in details the developments, the method is tested in the case of a superconducting cylinder submitted to a transverse magnetic field. The current density obtained is compared to another numerical technique (the semi-analytical method) in order to validate the results. Although not fully optimized yet, it appears that the proposed method is very stable, especially for large n-values (greater than 100).