  We consider the relativistic hydrodynamics of non-perfect fluids with the
goal of determining a formulation that is suited for numerical integration in
special-relativistic and general-relativistic scenarios. To this end, we review
the various formulations of relativistic second-order dissipative hydrodynamics
proposed so far and present in detail a particular formulation that is fully
general, causal, and can be cast into a 3+1 flux-conservative form as the one
employed in modern numerical-relativity codes. As an example, we employ a
variant of this formulation restricted to a relaxation-type equation for the
bulk viscosity in the general-relativistic magnetohydrodynamics code
$\texttt{BHAC}$. After adopting the formulation for a series of standard and
non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we
consider a novel general-relativistic scenario, namely, the stationary,
spherically symmetric viscous accretion onto a black hole. The newly developed
solution $-$ which can exhibit even considerable deviations from the inviscid
counterpart $-$ can be used as a testbed for numerical codes simulating
non-perfect fluids on curved backgrounds.
