"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
References
Footnotes
Figures
Tables