Induction heating is often used in metal processing for melting of alloys in induction furnaces, hardening of steel, etc. For chemically reactive alloys AC magnetic fields can help contain the melt in "semi-levitation" and "cold crucible" induction furnaces.

Unlike semilevitation, the liquid metal in a cold crusible can touch the water-cooled walls at which point the electric and magnetic fields undergo significant changes.

Computer modelling of the process can be very useful for its optimisation. The process involves several intertwined physical phenomena such as electromagnetic induction, heat transfer, phase change, elasto-plasticity, fluid flow with free surface, and magnetohydrodynamics.

The numerical model is based on PHYSICA and includes calculation of electric field, magnetic field, fluid flow, heat transfer and melting phase change. The solution procedures for the governing equations of the physical phenomena involved in the process are based on the principles of conservation of mass, momentum, energy and electric charge. In this work the finite volume method is used to discretise and solve the governing equations of electromagnetic induction. Such a formulation is compatible with the solution procedures for the other variables of the complex numerical model. The resulting computer code readily fits into the PHYSICA framework. It can also be used in combination with other finite volume codes based on unstructured meshes.