Numerical modelling of the free boundary problem in levitation melting under continuous casting conditions

A numerical model has been developed to solve the free boundary problem of electromagnetic levitation melting under continuous casting conditions. The free boundary problem has been solved to determine the equilibrium shape of the molten metal as a function of the operating inducting current in the system. The concept of domain derivative formalism has been applied to obtain minimization of the total energy functional of the system in a global framework to determine the free surface of the molten metal under levitated conditions. An iterative solution methodology has been formulated and the magnetic energy determined by using a boundary integral technique. Distribution of magnetic field has ben evaluated on the basis of the Biot-Savart law. The domain derivative approach is found to be a useful tool for faster convergence of the solution of the present free boundary problem. (C) Munksgaard, 1996.