Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T18:56:31.273Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of a converging cylindrical shock

Published online by Cambridge University Press:  12 April 2006

Gary A. Sod
Gary A. Sod
Affiliation:
Courant Institute of Mathematical Sciences, New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical proceure is introduced to solve the one-dimensional equations of gasdynamics for a cylindrically or spherically symmetric flow. The method consists of a judicious combination of Glimm's method and operator splitting. The method is applied to the problem of a converging cylindrical shock.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 4 , 21 December 1977 , pp. 785 - 794
Copyright
© 1977 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

Abarbanel, S. & Goldberg, M. 1972 Numerical solution of quasi-conservative hyperbolic systems — the cylindrical shock problem. J. Comp. Phys. 10, 1.Google Scholar
Chorin, A. J. 1976 Random choice solution of hyperbolic systems. J. Comp. Phys. 22, 517.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Interscience.
Glimm, J. 1965 Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697.Google Scholar
Godunov, S. K. 1959 Finite difference methods for numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sbornik. 47, 271.Google Scholar
Lapidus, A. 1971 Computation of radially symmetric shocked flows. J. Comp. Phys. 8, 106.Google Scholar
Payne, R. B. 1956 A numerical method for a converging cylindrical shock. J. Fluid Mech. 2, 185.Google Scholar
Perry, R. W. & Kantrowitz, A. 1951 The production and stability of converging shock waves. J. Appl. Phys. 22, 878.Google Scholar
Sod, G. A. 1976 The computer implementation of Glimm's method. Lawrence Livermore Lab. Rep. UCID-17252.Google Scholar
Sod, G. A. 1977 A survey of numerical methods for compressible fluids. J. Comp. Phys. (to appear). (See also New York Univ. ERDA & D. Rep. C00-3077–145.)Google Scholar