Accretion flows: Aspects of gas dynamic modeling

We present our view on the application of numerical models to accretion flo ws in astrophysics. Special attention is paid to the problem of existence o f steady-state solutions in time-dependent calculations and to origin of nu merically induced instabilities. The problem is considered of the supersoni c wind accretion onto gravitating objects. We also present the results of t he gas dynamic simulation of accretion on a body imitating the shape of the star magnetosphere with holes in its polar regions. This shape can occur a s a result of the cusp disintegration owing to the Rayleigh-Taylor instabil ity in the equatorial region of the magnetosphere.