  The early post-merger phase of a binary neutron-star coalescence is shaped by
characteristic rotational velocities as well as violent density oscillations
and offers the possibility to constrain the properties of neutron star matter
by observing the gravitational wave emission. One possibility to do so is the
investigation of gravitational wave damping through the bulk viscosity which
originates from violations of weak chemical equilibrium. Motivated by these
prospects, we present a comprehensive report about the implementation of the
self-consistent and second-order formulation of the equations of relativistic
hydrodynamics for dissipative fluids proposed by M\"uller, Israel and Stewart.
Furthermore, we report on the results of two test problems, namely the viscous
damping of linear density oscillations of isolated nonrotating neutron stars
and the viscous migration test, both of which confirm our implementation and
can be used for future code tests. Finally, we present fully
general-relativistic simulations of viscous binary neutron-star mergers. We
explore the structural and thermal properties of binary neutron-star mergers
with a constant bulk viscosity prescription and investigate the impact of bulk
viscosity on dynamical mass ejection. We find that inverse Reynolds numbers of
order $\sim 1\%$ can be achieved for the highest employed viscosity thereby
suppressing the dynamically ejected mass by a factor of $\sim 5$ compared to
the inviscid case.
