### 1.3 Plan of the review

This review is intended to provide a comprehensive discussion of different HRSC methods and of related
methods used in SRHD. However, we are not going to consider finite difference and finite volume
methods based on the usage of artificial viscosity techniques which are reviewed, e.g., in the
book of Wilson and Mathews [298]. Numerical methods for special relativistic MHD flows are
also not included as they are beyond the scope of this review. Furthermore, we do not include
numerical methods for general relativistic hydrodynamics. A comprehensive and recent discussion
of such methods can be found in another article in Living Reviews in Relativity written by
Font [91].
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 high-resolution
shock-capturing methods.

We have focussed on those aspects of the numerical methods more specific of SRHD, i.e., the discussion
of relativistic Riemann solvers and the computation of numerical fluxes. Some comments about the
extension to multi-dimensional flows are included in Section 9 (see below).

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 including the incorporation of general
equations of state is presented in Section 9.

The reader is assumed to have basic knowledge in classical [153, 62] and relativistic fluid dynamics [274, 8],
as well as in finite difference/volume methods for partial differential equations [237, 215]. A discussion of
modern finite volume methods for hyperbolic systems of conservation laws can be found, e.g.,
in [157, 160, 154]. The theory of spectral methods for fluid dynamics is developed in [42], and smoothed
particle hydrodynamics is reviewed in [199].