2006 Spring School on Numerical Methods
in Gravitation and Astrophysics
Download the lecture notes:
Lecture notes in Postscript
Lecture notes in PDF
Lecture notes in compressed Postscript
A nice introduction to numerical methods for relativistic hydrodynamics can be found in the introductory sections of these thesis
Computational Ultrarelativistic Hydrodynamics by Ian Hawke (compressed Postscript). It includes the spectral decomposition for the Roe solver in special relativity.
Extremely Relativistic Fluids in Strong-Field Gravity by David W Neilsen (compressed Postscript)
A Numerical Study of Relativistic Fluid Collapse by Scott C Noble (compressed Postscript)
Each provides a bit different perspective on the topics covered in the lecture notes and contains much more details and additional information.
The relativity.livingreviews.org is a good source of information on topics in relativity. These articles are particularly relevant to numerical relativistic hydrodynamics:
Numerical Hydrodynamics in Special Relativity It includes the spectral decomposition for the Roe solver in general relativity.
Numerical Hydrodynamics in General Relativity
An efficient method for finding the exact solutions of the relativistic Riemann problem is described in:
An Improved Exact Riemann Solver for Relativistic Hydrodynamics
An Improved Exact Riemann Solver for Multidimensional Relativistic Flows
Recent papers on numerical relativistic hydrodynamics