A numerical investigation is performed of the accretion of slowly rotating
matter onto a stellar magnetosphere. The shape of the magnetosphere is repr
esented by an impermeable, contracted dipole magnetic field surface with po
lar holes. Depending on the governing parameters, both steady-state solutio
ns with a system of discontinuities and unsteady flows with expanding shock
waves can be obtained. Certain solutions exhibit extended outflow regions.
The simulation is performed using a high-resolution finite volume numerica
l scheme and structured irregular grids adapted to the shape of the accreti
ng body.