Modelling of impulse loading in high‐temperature superconductors

Abstract

PurposeThe aim of this paper is to access performance of existing computational techniques to model strongly non‐linear field diffusion problems.Design/methodology/approachMultidimensional application of a finite volume front‐fixing method to various front‐type problems with moving boundaries and non‐linear material properties is discussed. Advantages and implementation problems of the technique are highlighted by comparing the front‐fixing method with computations using fixed grids. Particular attention is focused on conservation properties of the algorithm and accurate solutions close to the moving boundaries. The algorithm is tested using analytical solutions of diffusion problems with cylindrical symmetry with both spatial and temporal accuracy analysed.FindingsSeveral advantages are identified in using a front‐fixing method for modelling of impulse phenomena in high‐temperature superconductors (HTS), namely high accuracy can be obtained with a small number of grid points, and standard numerical methods for convection problems with diffusion can be utilised. Approximately, first order of spatial accuracy is found for all methods (stationary or mobile grids) for 2D problems with impulse events. Nevertheless, errors resulting from a front‐fixing technique are much smaller in comparison with fixed grids. Fractional steps method is proved to be an effective algorithm for solving the equations obtained. A symmetrisation procedure has to be introduced to eliminate a directional bias for a standard asymmetric split in diffusion processes.Originality/valueThis paper for the first time compares in detail advantages and implementation complications of a front‐fixing method when applied to the front‐type field diffusion problems common to HTS. Particular attention is paid to accurate solutions in the region close to the moving front where rapid changes in material properties are responsible for large computational errors.