Theoretical and numerical aspects of the system of equations of relativistic hydrodynamics.

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In astrophysics, general relativistic hydrodynamics plays a major role in the description of compact objects:

• Core-collapse supernovae.
• Gravitational collapse and black hole formation.
• Gamma-ray bursts.
• Relativistic jets.
• Coalescing binaries (BH/BH, BH/NS, NS/NS).
• Accretion.

The general relativistic hydrodynamic equations constitute a non-linear hyperbolic system of conservation laws.

Solid mathematical foundations and accurate numerical methodology, imported from Computational Fluid Dynamics: high-resolution shock-capturing (HRSC) schemes written in conservation form.

An online review on Numerical Hydrodynamics in General Relativity can be found in my article for the electronic journal Living Reviews in Relativity.

The group led by Prof. Ibánez (Valencia) has pioneered the extension of those techniques from Newtonian hydrodynamics to General Relativity.

CHRONOLOGY: from Special Relativity to General Relativity

• Font, Ibanez, Marquina, Martí
  Astronomy and Astrophysics, 282, 304-314 (1994)

• Donat, Font, Ibanez, Marquina
  Journal of Computational Physics, 146, 58-81 (1998)

• Banyuls, Font, Ibanez, Marti, Miralles
  Astrophysical Journal, 476, 221-233 (1997)
  3+1 formulation

• Pons, Font, Ibanez, Marti, Miralles
  Astronomy and Astrophysics, 339, 638-642 (1998)

• Font, Miller, Suen, Tobias
  Physical Review D, 61, 044011 (2000)
  3+1 3D Einstein-hydro code

• Papadopoulos, Font
  Physical Review D, 61, 024015 (2000)
  Fully covariant formulation

• Ibanez, Aloy, Font, Marti, Miralles, Pons
  Proceedings Godunov Methods: Theory and Applications,
  ed. E.F. Toro, Kluwer Academic/Plenum Publishers (2000)

The above references provide a complete theoretical framework for numerical applications, using HRSC schemes, in Relativistic Astrophysics, with dynamical spacetimes in General Relativity.