2 Special Relativistic Hydrodynamics1 Introduction1.2 Overview of the numerical

1.3 Plan of the review 

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. 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, 35Jump To The Next Citation Point In The Article] and relativistic fluid dynamics [171, 6Jump To The Next Citation Point In The Article], 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 [96Jump To The Next Citation Point In The Article, 98, 93]. The theory of spectral methods for fluid dynamics is developed in [24], and smoothed particle hydrodynamics (SPH) is reviewed in [121Jump To The Next Citation Point In The Article].



2 Special Relativistic Hydrodynamics1 Introduction1.2 Overview of the numerical

image Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr-1999-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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