  An implicit algorithm for solving the equations of general relativistic
hydrodynamics in conservative form in three-dimensional axi-symmetry is
presented. This algorithm is a direct extension of the pseudo-Newtonian
implicit radiative magnetohydrodynamical solver -IRMHD- into the general
relativistic regime.
  We adopt the Boyer-Lindquist coordinates and formulate the hydrodynamical
equations in the fixed background of a Kerr black hole. The set of equations
are solved implicitly using the hierarchical solution scenario (HSS). The HSS
is efficient, robust and enables the use of a variety of solution procedures
that range from a purely explicit up to fully implicit schemes. The
discretization of the HD-equations is based on the finite volume formulation
and the defect-correction iteration strategy for recovering higher order
spatial and temporal accuracies. Depending on the astrophysical problem, a
variety of relaxation methods can be applied. In particular the vectorized
black-white Line-Gauss-Seidel relaxation method is most suitable for modeling
accretion flows with shocks, whereas the Approximate Factorization Method is
for weakly compressible flows.
  The results of several test calculations that verify the accuracy and
robustness of the algorithm are shown. Extending the algorithm to enable
solving the non-ideal MHD equations in the general relativistic regime is the
subject of our ongoing research.
