Numerical Simulation of Shielding Current Density in High-Temperature Superconductor by Parallel Processing on PC Cluster

研究了高温超导体中屏蔽电流密度随时间变化的数值分析方法。虽然有限元法在工程的各个领域得到了广泛的应用，但它存在两个固有的困难：近似解的光滑性有限和单元生成耗时。为了解决这一难题，人们提出了几种无网格方法。本文在无网格方法的基础上开发了三维数值模拟程序，用于计算屏蔽电流密度的时间演化。为了使控制方程在空间和时间上离散化，分别采用了后向欧拉法和无单元伽辽金法。为了稳定求解产生的非线性系统，提出了自适应去加速牛顿法。此外，为了实现高性能计算，将MPI在PC集群上的并行处理应用于数值模拟。利用上述仿真方法，研究了感应法测量临界电流密度的方法。当高温超导体暴露在交流线圈电流产生的磁场中时，线圈中感应的电压不仅包含线性分量，而且包含高次谐波。谐波电压作为线圈电流的函数进行了数值计算。计算结果表明，当线圈电流超过一定极限时，三次谐波电压会突然被激发。此外，还发现三次谐波电压的平方根近似是线圈电流的线性函数。

The numerical method has been investigated for analyzing the time evolution of the shielding current density in the high-temperature superconductor. Although the finite element method has been widely used in the various fields of the engineering, it has been plagued by two inherent difficulties : the limited smoothness ofthe approximate solution and the time-consuming element generation. In order to resolve the difficulties, several meshless approaches have been proposed.In the present study, the 3D numerical simulation code has been developed on the basis of the meshless approach and it has been employed for calculating the time evolution of the shielding current density In order to discretize the governing equations with respect to space and time, the backward Euler method and the element free Galerkin method are employed, respectively. For the purpose of solving the resulting nonlinear system stably, the adaptively deaccelerated Newton method has been proposed. Furthermore, to achieve the high-performance computing, the parallel processing by using the MPI on a PC cluster is applied to the numerical simulation.By using the above simulation method, the inductive method for measuring the critical current density is investigated. When the high-temperature superconductor is exposed to the magnetic field generated by the ac coil current, the voltage induced in the coil contains not only a linear component but higher harmonics. The harmonic voltages are numerically calculated as a function of the coil current. The results of computations show that, above a certain limit of the coil current, The third harmonic voltage is suddenly excited. In addition, it is also found that the square root of the third harmonic voltage is approximately a linear function of the coil current.