  Characteristic methods show excellent promise in the evolution of single
black hole spacetimes. The effective coupling with matter fields may help the
numerical exploration of important astrophysical systems such as neutron star
black hole binaries. To this end we investigate formalisms for numerical
relativistic hydrodynamics which can be adaptable to null (characteristic)
foliations of the spacetime. The feasibility of the procedure is demonstrated
with one-dimensional results on the evolution of self-gravitating matter
accreting onto a dynamical black hole.
