Computational general relativistic astrophysics: The Neutron Star Grand Challenge Project

General Relativistic Astrophysics - astrophysics that involves strong and d ynamical gravitational fields requiring the full Einstein equations for its understanding - is becoming an exciting area of research, due to the large amount of data in high energy astronomy, and to the great promise of gravi tational wave astronomy. In particular, Computational General Relativistic Astrophysics, with the recent stunning increases in computer power, may hol d the key to the understanding of many observations in high energy astronom y and gravitational wave astronomy. The NASA Neutron Star Grand Challenge Project aims at developing a computat ional infrastructure for general relativistic astrophysics based on state-o f-the-art massively parallel computational technology. The numerical simula tion of coalescing neutron stars was chosen as the driving application of t he code development effort. In this paper we review the present status of t he project. The 3D code that contains the Einstein equations and the relati vistic hydrodynamic equations has recently passed the final milestone requi rement of the NASA project and has been released to the community with docu mentation. We propose a set of testing criteria for the validation of gener al relativistic hydrodynamic codes, and discuss some preliminary results ob tained with the code on the head-on collisions of neutron stars.