Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aas...20314103k&link_type=abstract
American Astronomical Society Meeting 203, #141.03; Bulletin of the American Astronomical Society, Vol. 36, p.587
Astronomy and Astrophysics
Astronomy
Scientific paper
The current fireball model of Gamma-Ray Bursts(GRBs) involves the ultra-relativistic hydrodynamics where the matter moves with the Lorentz factor γ =102-10^3. In order to investigate this high-γ ultra-relativistic hydrodynamics, various numerical algorithms have been developed. All these relativistic hydrodynamics codes are tested in the Riemann shock tube problem for which the analytic solution is known for simple cases. In this paper, we calculate the most general analytic solution of the special relativistic Riemann shock tube problem. This calculation has been done previously by MARTÍ and MÜLLER but their calculation of the shock jump conditions is in error. Furthermore, their Lorentz factor is not high enough to be applicable to GRB problems. We correct their results and expand the calculation to higher Lorentz factor up to γ =102-10^3 which is applicable to the GRB-related hydrodynamics codes. These results of the high-γ Riemann shock tube problem can provide the good test problem in which the future high-γ numerical calculations can be tested.
This work was supported by NASA Cooperative Agreement No. NCC 5-615.
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