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Numerical hydrodynamics in special relativity. (English) Zbl 1068.83502
Summary: This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Update to the author’s paper [Zbl 0944.83006]: Article revision.
Section 1: reorganized and slightly modified
Section 2.3: completely changed to discuss the exact solution of the Riemann problem in the more general case of arbitrary tangential velocities; Fig. 2 replaced; Figs. 3, 4 and Table 1: new
Section 6.2.1: discussion expanded; Tables 8, 9 and 10 (orig. 6, 7 and 8) expanded; Fig. 8 new
Section 7.1: (Applications: Astrophysical jets): updated (new figures and movies)
Section 7.2: (Applications: GRBs): updated (new figures and movies)
Section 7.3: (Relativistic Heavy Ion Collisions): new
Section 8.1: (Evaluation of the methods): discussion updated; Table 12 (orig. Table 10) updated
Section 8.2: (Present and future developments): substantially modified
Section 9.1: (Incorporation of complex EOS): new
Source codes: (Programs RIEMANN VT and RPPM): new
References: Number has increased from 198 to 308

MSC:
83A05 Special relativity
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83-08 Computational methods for problems pertaining to relativity and gravitational theory
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