Quasi-3D Discretization of Thermal Hot-Spot Propagation in Superconducting Models

To deal with the multi-scale nature of thermal hot-spot propagation in superconducting magnets, this work presents a quasi-three-dimensional (Q3D) approach combining a two-dimensional finite-element method (FEM) in the transversal cross-section of the magnet for resolving the geometrical details, with a one-dimensional spectral-element method based on orthogonal polynomials in longitudinal direction for accurately and efficiently representing steep temperature fronts. The Q3D formulation is elaborated and the idea is illustrated on a thermal benchmark problem. Finally, the method is validated against a conventional 3D simulation carried out by a commercial software. In terms of computational efficiency, it is shown that the proposed Q3D approach is superior to the conventional 3D FEM.