| Research Abstract |
Among the industrial applications of the high-Tc superconductor (HTS), the magnetic levitation and the magnetic shielding have recently become promising. Since the quantitative evaluation of the shielding current density is indispensable for the development of the magnetic levitation system and the magnetic shielding apparatus, the various methods have been so far proposed for calculating the time evolution of the shielding current density. However, in all of the methods, the finite element method (FEM) has been employed for the discretization of the governing equations.
In spite of the quite convenience, the FEM has been plagued by two inherent difficulties. First of all, the region has to be divided into a set of finite elements before using the FEM program. In general, the element generation is even more time-consuming than the assembly and the solution of the finite element equations. Second, the solution obtained by the FEM has a limitation in its smoothness. Even if the solution i
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s continuous, its derivative might be discontinuous across the element boundary. In the numerical simulation of the shielding current density, such a limited regularity of the solution leads to the discontinuous electric fields.
In order to resolve the above difficulties, several meshless approaches have been proposed : the DE method, the EFG method and the MLPG method. Since the finite elements of a geometrical structure are no longer necessary for all of the methods, the data preparation is significantly simplified.
By using the element-free Galerkin method, we have developed the 3D code to integrate the governing equations of the shielding current density in the HTS plate. After calculating the time evolution of the shielding current density by use of the code, we have performed the spectral analysis of the magnetic flux density. Conclusions obtained in the present study are summarized as follows :
1) For the case where the B-dependence of the flow resistivity and the critical current density is taken into account, the third harmonics of the magnetic flux density are rapidly excited with an increase in the amplitude of the applied ac magnetic field.
2) For the case where their B-dependence is neglected, an increase in the applied magnetic flux density will weaken the third harmonics.
From the above results, we might conclude that the rapid growth of the third harmonics is closely related to the B-dependence of the flow resistivity and the critical current density. Less
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