  Results of numerical simulations of shock solutions in a geometrical thin
accretion disk around a Kerr black hole (BH) are presented. Using the smoothed
particle hydrodynamics (SPH) technique, the influence of the central object is
included by means of an effective potential, We first present the theory of
standing shock formation in accretion disks around a Kerr black hole, and show
that the results of our numerical simulation agree very well with the
theoretical results. We find that the shocks in an inviscid flow are very
stable. We also remove the ambiguity prevalent regarding the location and
stability of shocks in adiabatic flows. Finally we sketch some of the
astrophysical consequences of our findings in relation to accretion disks in
Active Galactic Nuclei (AGN) and Quasars.
