Contributions to the mathematical study of some problems in magnetohydrodynamics and induction heating

The aim of the work is to numerically simulate an induction furnace in order to understand its behavior and to predict its performance under the variation of some parameters. An axisymmetric mathematical model consisting of coupled electromagnetic, hydrodynamic and thermal submodels is written before discretization. The thermal and hydrodynamic submodels are discretized by means of Lagrange- Galerkin methods, whereas the electromagnetic submodel is discretized with a mixed boundary element/ finite element method. Iterative algorithms are also introduced to deal with the nonlinearities and the coupling terms. Numerical results of the simulation of an industrial induction furnace for melting are presented.