Living Reviews in Relativity

"Numerical Hydrodynamics and Magnetohydrodynamics
in General Relativity"
by
José A. Font  

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Abstract
1 Introduction
2 Equations of General-Relativistic Hydrodynamics
2.1 Spacelike (3+1) approaches
2.2 Covariant approaches
2.3 Going further: beyond ideal hydrodynamics
3 Equations of General-Relativistic Ideal Magnetohydrodynamics
3.1 Numerical approaches
3.2 Recovery of primitive variables
3.3 Going further
4 Numerical Schemes
4.1 Finite difference schemes
4.2 Other techniques
4.3 The magnetic-field divergence-free constraint
4.4 State-of-the-art three-dimensional codes
5 Hydrodynamic and Magnetohydrodynamic Simulations in Relativistic Astrophysics
5.1 Gravitational collapse
5.2 Accretion on to black holes
5.3 Hydrodynamic and magnetohydrodynamic evolution of neutron stars
6 Additional Information
6.1 Riemann problems in locally-Minkowskian coordinates
6.2 Characteristic fields in the 3+1 conservative Eulerian formulation of Section 2.1.3
7 Acknowledgments
Open References References
Footnotes
Figures
Tables