Computation of Magnetically-Supported Free Surface by a Coupled Finite/Boundary Element Method

A computational methodology based on the coupled finite element and boundary methods is developed to predict the free surface shapes of electrically conducting liquids supported by the electromagnetic field. The work is an extension of our previous FEIBE model for induction calculations. The free surface algorithm is developed using the Weighted Residual Method, the very same used for nonlinear finite element formulation. This allows the treatment of field computation and free surface prediction in the same manner, thus making easier the formulation of the magnetically-supported free surface problems. Like other nonlinear algorithms, the boundary/finite element free surface scheme is also iterative owing to the fact that free surface shapes are unknown a priori. But the numerical scheme is robust and efficient and is capable of handling rather complex free surface deformations. Computational algorithms will be given and are tested by comparing with other solutions whenever available. Computed results of magnetically-supported free surface shapes are presented for magnetic levitation under microgravity and floating zone refining processes under normal gravity.