Hostname: page-component-5c6d5d7d68-qks25 Total loading time: 0 Render date: 2024-08-22T23:17:00.322Z Has data issue: false hasContentIssue false
  • English
  • Français

The special relativistic shock tube

Published online by Cambridge University Press:  21 April 2006

Kevin W. Thompson
Kevin W. Thompson
Affiliation:
Space Science Division, NASA Ames Research Center, Moffett Field, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The shock-tube problem has served as a popular test for numerical hydrodynamics codes. The development of relativistic hydrodynamics codes has created a need for a similar test problem in relativistic hydrodynamics. The analytical solution to the special relativistic shock-tube problem is presented here. The relativistic shock-jump conditions and rarefaction solution which make up the shock tube are derived. The Newtonian limit of the calculations is given throughout.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 365 - 375
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Centrella, J. & Wilson J. R.1984 Planar numerical cosmology. II. The difference equations and numerical tests. Astrophys. J. Suppl. 54, 229.Google Scholar
Lightman A. P., Press W. H., Price, R. H. & Teukolsky S. A.1975 Problem Book in Relativity and Gravitation. pp. 230–232. Princeton University Press.
Mathews W. G.1971 The hydromagnetic free expansion of a relativistic gas. Astrophys. J. 165, 147–164.Google Scholar
Sod G. A.1978 A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comp. Phys. 27, 1–31.Google Scholar
Taub A. H.1948 Relativistic Rankine-Hugoniot Equations. Phys. Rev. 74, 328–334.Google Scholar
Taub A. H.1967 Relativistic hydrodynamics. In Relativity Theory and Astrophysics 1. Relativity and Cosmology (ed. J. Ehlers), pp. 170–193. American Mathematical Society, Providence RI.
Thompson K. W.1985 A two dimensional model for relativistic gas jets. Ph.D. thesis, Princeton University.