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).