We describe a numerical ionosphere-magnetosphere coupling model with a relationship between the field-aligned potential drop and the ionospheric conductivities. A two-dimensional incompressible magnetohydrodynamic (MHD) model for the magnetosphere, field lines with finite resistivity, a ''2 1/2'' dimensional ionosphere, as well as a phenomenological modeling of the ionization process are integrated in a time-dependent fluid simulation code. We discuss the algorithm and the validity of the results and give an example run with possible application to eastward drifting &OHgr; bands of the morning sector. Our model is valid for time scales longer than the Alfv¿n bounce time and for spatial scales roughly between 10 and 1000 km. It is found that the inhomogeneous ionospheric conductivities affect the system dynamics substantially. This feature is essential when the model is used to study the development of auroral forms. ¿ American Geophysical Union 1993