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Numerical hydrodynamics in general relativity. (English) Zbl 1068.83501
Summary: 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.
Update to the author’s paper [Zbl 0944.83007]: 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.

MSC:
83-08 Computational methods for problems pertaining to relativity and gravitational theory
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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