The review is organized as follows: Section
2
contains a derivation of the equations of special relativistic
(perfect) fluid dynamics, as well as a discussion of their main
properties. In Section
3
the most recent developments in numerical methods for SRHD are
reviewed paying particular attention to highresolution
shockcapturing methods. Other developments in special
relativistic numerical hydrodynamics are discussed in
Section
4
. Numerical results obtained with different methods as well as
analytical solutions for several test problems are presented in
Section
6
. Two astrophysical applications of SRHD are discussed in
Section
7
. An evaluation of the various numerical methods is given in
Section
8
together with an outlook for future developments. Finally, some
additional technical information is presented in Section
9
.
The reader is assumed to have basic knowledge in
classical [92,
35] and relativistic fluid dynamics [171,
6], as well as in finite difference / volume methods for
partial differential equations [152,
132]. A discussion of modern finite volume methods for hyperbolic
systems of conservation laws can be found, e.g., in [96,
98,
93]. The theory of spectral methods for fluid dynamics is developed
in [24], and smoothed particle hydrodynamics (SPH) is reviewed
in [121].

Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr19993
© MaxPlanckGesellschaft. ISSN 14338351
Problems/Comments to
livrev@aeipotsdam.mpg.de
