  In this paper, the general procedure to solve the General Relativistic
Hydrodynamical(GRH) equations with Adaptive-Mesh Refinement (AMR) is presented.
In order to achieve, the GRH equations are written in the conservation form to
exploit their hyperbolic character. The numerical solutions of general
relativistic hydrodynamic equations are done by High Resolution Shock Capturing
schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of
conservation laws. These schemes depend on the characteristic information of
the system. The Marquina fluxes with MUSCL left and right states are used to
solve GRH equations. First, different test problems with uniform and AMR grids
on the special relativistic hydrodynamics equations are carried out to verify
the second order convergence of the code in 1D, 2D and 3D. Results from uniform
and AMR grid are compared. It is found that adaptive grid does a better job
when the number of resolution is increased. Second, the general relativistic
hydrodynamical equations are tested using two different test problems which are
Geodesic flow and Circular motion of particle In order to this, the flux part
of GRH equations is coupled with source part using Strang splitting. The
coupling of the GRH equations is carried out in a treatment which gives second
order accurate solutions in space and time.
