Vol. 6 (2003) > lrr-2003-4

doi: 10.12942/lrr-2003-4
Living Rev. Relativity 6 (2003), 4

Numerical Hydrodynamics in General Relativity

1 Departamento de Astronomía y Astrofísica, Edificio de Investigación "Jeroni Muñoz", Universidad de Valencia, Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain

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Article Abstract

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.


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Article Citation

Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

José A. Font,
"Numerical Hydrodynamics in General Relativity",
Living Rev. Relativity 6,  (2003),  4. URL (cited on <date>):

Article History

ORIGINAL http://www.livingreviews.org/lrr-2000-2
Title Numerical Hydrodynamics in General Relativity
Author José A. Font
Date accepted 28 March 2000, published 8 May 2000
UPDATE http://www.livingreviews.org/lrr-2003-4
Title Numerical Hydrodynamics in General Relativity
Author José A. Font
Date accepted 6 May 2003, published 19 August 2003
Changes Article revision. Sections 3 and 4 have undergone substantial changes and have been considerably enlarged; almost all sections have been updated. The number of references has been extended from previous 241 to the current 319.
UPDATE http://www.livingreviews.org/lrr-2008-7
Title Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Author José A. Font
Date accepted 21 July 2008, published 19 September 2008
Changes The title has been changed to emphasize that numerical magnetohydrodynamics (MHD) is now also reviewed.

The abstract has been changed accordingly, regarding the MHD aspects of the new version.

The sectioning in Section 2 is unchanged, yet the contents may have seen slight updates wherever necessary.

Section 3 on MHD is entirely new.

Section 4 (which was Section 3 in the previous version) has seen changes throughout (new text and new descriptions to account for recent developments) along with new additions.
The Section 3.2.3 in the previous version of the article has been removed and some of its contents have been moved into the "going further" section (Section 4.2.3 in the updated version of the article). Section 4.3 on the magnetic field divergence-constraint is entirely new. Section 4.4. on state-of-the-art codes has undergone major changes with respect to the corresponding Section 3.3. of the previous version of the article. This section is splitted into two main subsections, each one of them devoted to describing hydrodynamical and MHD codes, respectively. Major updates have occurred in each of these subsections and two tables have been added.

Section 5 on astrophysical applications has been widely updated and enlarged to accommodate the spectacular level of activity witnessed in the field in recent years, both regarding hydrodynamics and MHD. While the basic subsectioning of this section still coincides (broadly speaking) with that of the previous version of the article, major modifications and additions have occurred throughout regarding the contents. In general, the description of one-dimensional studies has been reduced to limit the length of the article. The previous Section 4.1.2 on critical collapse has been removed. New figures and animations have been added, in particular those appearing in Figures 7, 8, 9, 11, 13, 16, and 18 (where the numbering here applies to the revised version of the article).

The reference list has been noticeably enlarged.
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