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Intrinsically stable magnetic levitation between superconductors andpermanent magnets can be exploited in a variety of applications of greattechnical interest in the field of transportation (rail transportation), energy(flywheels) and industry. In this contribution, we present a new model for thecalculation of levitation forces between superconducting bulks and permanentmagnet, based on the $H$-formulation of Maxwell's equations coupled with anArbitrary Lagrangian-Eulerian formulation. The model uses a moving mesh thatadapts at each time step based on the time-change of the distance between asuperconductor bulk and a permanent magnet. The model is validated against afixed mesh model (recently in turn validated against experiments) that uses ananalytical approach for calculating the magnetic field generated by the movingpermanent magnet. Then, it is used to analyze the magnetic field dynamics bothin field-cooled and zero-field-cooled conditions and successively used to testdifferent configurations of permanent magnets and to compare them in terms oflevitation forces. The easiness of implementation of this model and itsflexibility in handling different geometries, material properties, andapplication scenarios make the model an attractive tool for the analysis andoptimization of magnetic levitation-based applications.

Dynamic modeling of levitation of a superconducting bulk by coupled $H$-magnetic field and Arbitrary Lagrangian-Eulerian formulations