Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T06:27:01.553Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on the structure of viscous and numerically-captured shocks

Published online by Cambridge University Press:  04 July 2016

J. Pike
Get access Rights & Permissions [Opens in a new window]

Summary

An exact expression for the flow variables through a viscous shock wave is obtained from the Navier-Stokes equations. The Prandtl number is taken to be ¾, which is close to the value for air, and the viscosity is assumed to be given by Sutherland's formula.

By considering the limit as the viscosity tends to zero, it is shown that the solution to the Euler equations has an entropy spike at the shock wave. This explains certain, hitherto considered spurious, features of shock waves captured by numerical solutions of the Euler equations.

Type
Research Article
Information
The Aeronautical Journal , Volume 89 , Issue 889 , November 1985 , pp. 335 - 338
Copyright
Copyright © Royal Aeronautical Society 1985 

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.)

Footnotes

*

The research reported in this paper was carried out while the author was at RAE, Bedford.

References

1. Becker, R. Stobewelle und Detonation. Z. Phys, 1921,8,321.Google Scholar
2. Thomas, L. H. Note on Becker's theory of the Shock Front. J Chem Phys, 1944,12,449–53.Google Scholar
3. Morduchow, M. and Libby, P. A. On a complete solution of the one-dimensional flow equations of a viscous, heatconducting, compressible gas. J Aero Soc, 1949,16,11,674.Google Scholar
4. Gilbarg, D. and Paolucci, D. The structure of shock waves in the continuum theory of fluids. J ofRational Mech Anal, 1953,2, 617.Google Scholar
5. Howarth, L. Modern developments in fluid dynamics, high speed flow. Oxford University Press, 1953,1.Google Scholar
6. Liepmann, H. W., Narisima, R. and Chahine, M. T. Structure of a plane shock layer. Phy of Fluids, November 1962, 5, 11, 1313–24.Google Scholar
7. Hicks, B. L., Yen, S. M. and Reilly, B. J. The internal structure of Shockwaves. J FluidMech, 1972,53,1,85–111.Google Scholar
8. Pia, S. Viscous flow theory, 1 Laminar flow, D. Van Nostrand Co Inc. 1956.Google Scholar
9. Von Neumann, J. and Richtmyer, R. D. A method for the numerical calculation of hydrodynamic shocks. J of Applied Phy, March 1950, 21, 3,232–237.Google Scholar
10. Roe, P. L. An introduction to numerical methods suitable for the Euler equations. VKI Lecture Series Note, An introduction to computational fluid dynamics, 1983-01.Google Scholar
11. Rizzi, A. and Viviand, H. Numerical methods for the computation of inviscid transonic flows with shock waves. Proceedings of the GAMM Workshop, Stockholm 1979. Vieweg 1981.Google Scholar