  We present time-dependent solutions of thin, supersonic accretion flows near
a black hole and compare them with analytical solutions. Such flows of
inviscid, adiabatic gas are characterized by the specific angular momentum and
the specific energy. We confirm that for a wide range of above parameters a
stable standing shock wave with a vortex inside it forms close to the black
hole. Apart from steady state solutions, we show the existence of non-steady
solutions for thin accretion flows where the accretion shock is destroyed and
re-generated periodically. The unstable behavior should be caused by
dynamically induced instabilities, since inviscid, adiabatic gas is considered.
We discuss possible relevance of the periodic behavior on quasi-periodic
oscillations (QPOs) observed in galactic and extragalactic black hole
candidates.
