Magnetic induction and electric potential solvers for incompressible MHD flows

This work describes the theoretical background and the implementation of OpenFOAM solvers suitable for the simulation of incompressible magneto-hydrodynamic (MHD) flows. This class is a topic of interest for many research activities and industrial applications including nuclear fusion reactors, materials engineering and metallurgy. The main purpose of this document is to help the reader to get accustomed with the relevant phenomena and peculiar challenges of this kind of problems. In order to accomplish this goal it will focus the attention on the 2D MHD flows that arise in a rectangular duct with walls of arbitrary electrical conductivity when an electric conductive fluid moves in the presence of a transverse magnetic field.