The influence of radiative effects on the accretion onto stellar magnetospheres is investigated by performing global 2and 2.5-dimensional simulations on the basis of high-resolution numerical schemes with the application of irregular grids adapted to the shape of the magnetopause. The latter is represented by an impermeable, contracted dipole magnetic field surface with polar holes. Accreting matter is assumed to be optically thin. The physical mechanisms which are taken into account include

more »

... ling due to free-free and free-bound transitions, the Compton heating via X-ray scattering on electrons, and the inverse Compton cooling in the regions where the temperature of the matter becomes sufficiently large to be able to transfer part of its internal energy to photons. Depending on the determining parameters, both steady-state solutions with a system of discontinuities and unsteady flows with expanding shock waves can be obtained. It is shown that efficient cooling of the matter can substantially facilitate the penetration of the matter through the polar holes. The detailed consideration of the realistic radiative effects proved to be of great importance in our understanding of the accretion phenomenon, since they can substantially affect it both qualitatively and quantitatively.