  We have developed a new computer code, RELDAFNA, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite volume Godunov scheme using the full characteristic
decomposition of the SRHD equations, to achieve second and third order accuracy
in space (both PLM and PPM reconstruction). For time integration, we use the
method of directional splitting with symmetrization, which is second order
accurate in time. We have also implemented second and third order Runge-Kutta
time integration scheme for comparison. In addition to the hydrodynamics
solvers we have implemented approximate Riemann solvers along with an exact
Riemann solver. We examine the ability of RELDAFNA to accurately simulate
special relativistic flows efficiently in number of processors, computer memory
and over all integration time. We show that a wide variety of test problems can
be solved as accurately as solved by higher order programs, such as RAM,
GENESIS, or PLUTO, but with a less number of variables kept in memory and
computer calculations than most schemes, an advantage which is crucial for 3D
high resolution simulations to be of practical use for scientific research in
computational astrophysics. RELDAFNA has been tested in one, two and three
dimensions and in Cartesian, cylindrical and spherical geometries. We present
the ability of RELDAFNA to assist with the understanding of open questions in
high energy astrophysics which involve relativistic flows.
