超导块材悬浮的$H$ -磁场耦合动力学模型及任意拉格朗日-欧拉方程
Dynamic modeling of levitation of a superconducting bulk by coupled $H$-magnetic field and Arbitrary Lagrangian-Eulerian formulations
摘要：
超导体和永磁体之间的内在稳定的磁悬浮可以在运输（轨道运输）、能源（飞轮）和工业领域中具有巨大技术兴趣的各种应用中被利用。在这篇文章中，我们提出了一个新的模型计算超导块材和永磁体之间的悬浮力，基于$H$ -制定的麦克斯韦方程组耦合任意拉格朗日-欧拉制定。该模型使用了一个移动的网格，适应在每个时间步长的基础上的超导体块和永磁体之间的距离的时间变化。该模型是针对一个固定的网格模型（最近反过来验证实验），使用分析方法计算的磁场产生的移动永磁体。然后，它是用来分析的磁场动力学都在场冷却和零场冷却条件下，并相继用于测试不同配置的永磁体，并比较它们的悬浮力。该模型易于实现，在处理不同的几何形状，材料特性和应用场景的灵活性，使该模型的磁悬浮为基础的应用程序的分析和优化的一个有吸引力的工具。
英文摘要：
Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and industry. In this contribution, we present a new model for the calculation of levitation forces between superconducting bulks and permanent magnet, based on the $H$-formulation of Maxwell's equations coupled with an Arbitrary Lagrangian-Eulerian formulation. The model uses a moving mesh that adapts at each time step based on the time-change of the distance between a superconductor bulk and a permanent magnet. The model is validated against a fixed mesh model (recently in turn validated against experiments) that uses an analytical approach for calculating the magnetic field generated by the moving permanent magnet. Then, it is used to analyze the magnetic field dynamics both in field-cooled and zero-field-cooled conditions and successively used to test different configurations of permanent magnets and to compare them in terms of levitation forces. The easiness of implementation of this model and its flexibility in handling different geometries, material properties, and application scenarios make the model an attractive tool for the analysis and optimization of magnetic levitation-based applications.
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