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Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic...

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Autor principal: Font, José A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2008
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256108/
https://www.ncbi.nlm.nih.gov/pubmed/28179823
http://dx.doi.org/10.12942/lrr-2008-7
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author Font, José A.
author_facet Font, José A.
author_sort Font, José A.
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description This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. 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 in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at 10.12942/lrr-2008-7.
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spelling pubmed-52561082017-02-06 Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity Font, José A. Living Rev Relativ Review Article This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. 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 in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at 10.12942/lrr-2008-7. Springer International Publishing 2008-09-19 2008 /pmc/articles/PMC5256108/ /pubmed/28179823 http://dx.doi.org/10.12942/lrr-2008-7 Text en © The Author(s) 2008
spellingShingle Review Article
Font, José A.
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title_full Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title_fullStr Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title_full_unstemmed Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title_short Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
title_sort numerical hydrodynamics and magnetohydrodynamics in general relativity
topic Review Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256108/
https://www.ncbi.nlm.nih.gov/pubmed/28179823
http://dx.doi.org/10.12942/lrr-2008-7
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