Evolving black hole-neutron star binaries in general relativity using   pseudospectral and finite difference methods
  We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation. 
Matthew D. Duez, Francois Foucart, Lawrence E. Kidder, Harald P.   Pfeiffer, Mark A. Scheel, Saul A. Teukolsky