In a rotary magnetic refrigerator, a porous ring is turning in and out of a magnetic field region. At the outlet the adiabatic demagnetization of the magnetocaloric material (refrigerant) produces the "cold energy". The induced cold is described by a corresponding discontinuous temperature decrease, known as adiabatic temperature difference. For such a machine a sophisticated physical model has been developed, based on a mapping of the magneto-thermodynamic problem from a cylinder onto two rectangles. In this model, in a basic centre cell, two coupled linear partial differential equations are solved, which have been programmed in the Modelica language. To determine the performance of a two-stage magnetic refrigerator, an ensemble of this new designed centre module and some other recently created auxiliary modules are coupled with standard components from a Dymola thermal library, as e.g. pumps, ordinary heat exchangers, tubes, pipes, etc. The operation of a magnetic refrigerator is simulated with numerous parameters. Steady state solutions are obtained to verify the coefficient of performance under stable operation conditions. Optimal running conditions - defined by maximal values of the coefficient of performance - are not presented in this article, but can now easily be obtained with the existing program. Finally, a regulation strategy is proposed and implemented into the Dymola-Modelica program.