  (Abridged) We here continue our effort to model the behaviour of matter when
orbiting or accreting onto a generic black hole by developing a new numerical
code employing advanced techniques geared solve the equations of in
general-relativistic hydrodynamics. The new code employs a number of
high-resolution shock-capturing Riemann-solvers and reconstruction algorithms,
exploiting the enhanced accuracy and the reduced computational cost of AMR
techniques. In addition, the code makes use of sophisticated ray-tracing
libraries that, coupled with general-relativistic radiation-transfer
calculations, allow us to compute accurately the electromagnetic emissions from
such accretion flows. We validate the new code by presenting an extensive
series of stationary accretion flows either in spherical or axial symmetry and
performed either in 2D or 3D. In addition, we consider the highly nonlinear
scenario of a recoiling black hole produced in the merger of a supermassive
black hole binary interacting with the surrounding circumbinary disc. In this
way we can present, for the first time, ray-traced images of the shocked fluid
and the light-curve resulting from consistent general-relativistic
radiation-transport calculations from this process. The work presented here
lays the ground for the development of a generic computational infrastructure
employing AMR techniques to deal accurately and self-consistently with
accretion flows onto compact objects. In addition to the accurate handling of
the matter, we provide a self-consistent electromagnetic emission from these
scenarios by solving the associated radiative-transfer problem. While magnetic
fields are presently excluded from our analysis, the tools presented here can
have a number of applications to study accretion flows onto black holes or
neutron stars.
