Excision methods for high resolution shock capturing schemes applied to   general relativistic hydrodynamics
  We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of Reconstruction-Evolution methods, a standard class of HRSC methods. We test three different reconstruction schemes, namely TVD, PPM and ENO. The method does not require that the coordinate system is adapted to the excision boundary. We demonstrate the effectiveness of our method using tests containing discontinuites, static test-fluid solutions with black holes, and full dynamical collapse of a neutron star to a black hole. A modified PPM scheme is introduced because of problems arisen when matching excision with the original PPM reconstruction scheme. 
Ian Hawke, Frank L\"offler, Andrea Nerozzi