Abstract
It has become increasingly important to calculate magneto-hydrodynamics (MHD) flows under alternating-current (AC) magnetic fields, in order to control the molten metal processing step in the furnace by electromagnetic force. In this paper, three dimensional problems for an arbitrary-shape model are solved by using the hybrid finite element method-boundary element method (FEM-BEM) with the A-φ (magnetic vector potential-electric scalar potential) method in the electromagnetic field and using the arbitrary Lagrangian Eulerian-finite element method (ALE-FEM) in the velocity field with a free surface. The strong point of the ALE method is that the element itself moves along the velocity field of the fluid, and consequently, the boundary between the fluid and air is distinct. Using these methods, we can observe the complicatedly tangled physical parameters of the electromagnetic field in the cold crucible and confirm the unique shape and vibration of the surface of the molten metal.
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