  We discuss the equations describing the motion of ferrofluids subject to an
external magnetic field. We concentrate on the model proposed by R. Rosensweig,
provide an appropriate definition for the effective magnetizing field, and
explain the simplifications behind this definition. We show that this system is
formally energy stable, and devise a numerical scheme that mimics the same
stability estimate. We prove that solutions of the numerical scheme always
exist and, under further simplifying assumptions, that the discrete solutions
converge. We also discuss alternative formulations proposed in pre-existing
work, primarily involving a regularization of the magnetization equation and
supply boundary conditions which lead to an energy stable system. We present a
series of numerical experiments which illustrate the potential of the scheme in
the context of real applications.
