Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T06:44:31.484Z Has data issue: false hasContentIssue false
  • English
  • Français

The von Neumann paradox for the diffraction of weak shock waves

Published online by Cambridge University Press:  26 April 2006

P. Colella  and
L. F. Henderson
P. Colella
Affiliation:
Mail Stop L-316, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550, USA
L. F. Henderson
Affiliation:
Mail Stop L-316, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550, USA Permanent address: Department of Mechanical Engineering, University of Sydney, NSW 2006, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

We present results from our experiments with the irregular reflection of shock waves in argon. We compare the data with the results we obtained numerically; the assumptions for the computational code were that we had unsteady, two-dimensional, compressible, inviscid, flow of a perfect gas. When precautions were taken to reduce the effects of the gas viscosity on the experimental data, we obtained very good agreement between the numerical and the experimental results for the ramp Mach number and the trajectory path triple-point angle, but there were discrepancies with the wave-angle data. The discrepancies were ascribed to the sensitivity of the data to both viscosity and to a singularity. We show that there are actually two weak irregular wave reflections, namely a classic Mach reflection (MR) and a new type, that we call a von Neumann reflection (NR). The structure of the NR is discussed in some detail, and so are the transition criteria for the various wave systems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 71 - 94
Copyright
© 1990 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

Ames Research Staff 1953 Equations, tables and charts for compressible flow. NACA Ref. 1135.
Berger, M. & Colella, P. 1987 Adaptive mesh refinement for shock hydrodynamics. Lawrence Livermore National Laboratory, Preprint UCRL 97196, to appear in J. Comp. Phys.Google Scholar
Birkhoff, G. 1950 Hydrodynamics, A Study in Logic, Fact and Similitude. Princeton University Press.
Bleakney, W. & Taub, A. H. 1949 Rev. Mod. Phys. 21, 584–605.
Chern, I. L. & Colella, P. 1987 A conservative front tracking method for hyperbolic conservation laws. Lawrence Livermore National Laboratory, Preprint UCRL-97200.
Colella, P. 1984 Multidimensional upwind methods for hyperbolic conservation laws. Lawrence Berkeley Lab. Rep. LBL-17023, to appear in J. Comp. Phys.Google Scholar
Colella, P. & Woodward, P. R. 1984 J. Comp. Phys. 54, P175–201.
Glaz, H. M., Colella, P., Glass, I. & Deschambault, R. 1985 Proc. Roy. Soc. Lond. A 398, P117–140
Henderson, L. F. 1987 Z. angew. Math. Mech. 67, 73–86.
Henderson, L. F. & Gray, P. M. 1981 Proc. Roy. Soc. Lond. A 377, 363–378
Henderson, L. F. & Lozzi, A. 1975 J. Fluid Mech. 68, 139–155.
Henderson, L. F. & Lozzi, A. 1979 J. Fluid Mech. 94, 541–560.
Henderson, L. F. & Siegenthaler, A. 1980 Proc. Roy. Soc. Lond. A 369, 537–555
Hornung, H. G. & Kychakoff, G. 1977 Proc. 11th Intl Symp. Shock Tubes & Waves, Seattle, pp. 296–302.
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 J. Fluid Mech. 90, 541–560.
Hornung, H. G. & Robinson, M. H. 1982 J. Fluid Mech. 123, 155–164.
Hornung, H. G. & Taylor, J. R. 1982 J. Fluid Mech. 123, 143–153.
Johannesen, N. H. & Hodgson, J. P. 1979 Rept. Prog. Phys. 42, 629–676.
Kawamura, R. & Saito, H. 1956 J. Phys. Soc. Japan 11, 584–542.
Leer, B. Van 1979 J. Comp. Phys. 32, 276–303.
Mölder, S. 1971 CASI Trans. 4, 73–80.
Neumann, J. Von 1943 See Collected Works, vol. 6, 1963. Pergamon.
Pantazapol, D., Bellett, J. C. & Soustre, J. 1972 C.R. Acad. Sci. Paris, A 255, 275g.
Woodward, R. R. & Colella, P. 1984 J. Comp. Phys. 54, 115–174.