Living Rev. Relativity, 6, (2003), 7, 100 pp. [Online Article].
Published by the Max Planck Institute for Gravitational Physics
Albert Einstein Institute, Germany.
This review is conceed 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 ID relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate ID relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Contents.
ntroduction.
Special Relativistic Hydrodynamics.
High-Resolution Shock-Capturing Methods.
Other Developments.
Summary of Methods.
Test Bench.
Applications.
Conclusion.
Additional Information.
Algorithms to recover primitive quantities.
Spectral decomposition of the 3D SRHD equations.
Programs.
References.
This review is conceed 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 ID relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate ID relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Contents.
ntroduction.
Special Relativistic Hydrodynamics.
High-Resolution Shock-Capturing Methods.
Other Developments.
Summary of Methods.
Test Bench.
Applications.
Conclusion.
Additional Information.
Algorithms to recover primitive quantities.
Spectral decomposition of the 3D SRHD equations.
Programs.
References.