Living Reviews in Relativity

"Numerical Hydrodynamics in Special Relativity"
by
José Maria Martí and Ewald Müller  

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Abstract
1 Introduction
1.1 Current fields of research
1.2 Overview of the numerical methods
1.3 Plan of the review
2 Special Relativistic Hydrodynamics
2.1 Equations
2.2 SRHD as a hyperbolic system of conservation laws
2.3 Exact solution of the Riemann problem in SRHD
3 High-Resolution Shock-Capturing Methods
3.1 Relativistic PPM
3.2 Relativistic Glimm’s method
3.3 Two-shock approximation for relativistic hydrodynamics
3.4 Roe-type relativistic solvers
3.5 Falle and Komissarov upwind scheme
3.6 Relativistic HLL method (RHLLE)
3.7 Artificial wind method
3.8 Marquina’s flux formula
3.9 Symmetric TVD, ENO schemes with nonlinear numerical dissipation
4 Other Developments
4.1 Van Putten’s approach
4.2 Relativistic SPH
4.3 Relativistic beam scheme
5 Summary of Methods
6 Test Bench
6.1 Relativistic shock heating in planar, cylindrical and spherical geometry
6.2 Propagation of relativistic blast waves
7 Applications
7.1 Astrophysical jets
7.2 Gamma-ray bursts (GRBs)
7.3 Relativistic heavy ion collisions (RHIC)
8 Conclusion
8.1 Evaluation of the methods
8.2 Present and future developments
9 Additional Information
9.1 Incorporation of complex equations of state
9.2 Algorithms to recover primitive quantities
9.3 Spectral decomposition of the 3D SRHD equations
9.4 Programs
9.5 Basics of HRSC methods
9.6 Newtonian SPH equations
Open References References
Footnotes
Figures
Tables