  Many of the recent numerical simulations of binary black holes in vacuum
adopt the moving puncture approach. This successful approach avoids the need to
impose numerical excision of the black hole interior and is easy to implement.
Here we wish to explore how well the same approach can be applied to moving
black hole punctures in the presence of relativistic hydrodynamic matter.
First, we evolve single black hole punctures in vacuum to calibrate our BSSN
(Baumgarte-Shapiro-Shibata-Nakamura) implementation and to confirm that the
numerical solution for the exterior spacetime is invariant to any ``junk''
(i.e., constraint-violating) initial data employed in the black hole interior.
Then we focus on relativistic Bondi accretion onto a moving puncture
Schwarzschild black hole as a numerical testbed for our high-resolution
shock-capturing relativistic hydrodynamics scheme. We find that the
hydrodynamical equations can be evolved successfully in the interior without
imposing numerical excision. These results help motivate the adoption of the
moving puncture approach to treat the binary black hole-neutron star problem
using conformal thin-sandwich initial data.
