Abstract
For the case of initially infinitesimally weak spherically and cylindrically imploding shocks, Ponchaut et al. (J. Fluid Mech., 560:102–122, 2006) recently obtained universal solutions. We study the effect of starting the shock with an initially finite strength on the trajectory of the shock by performing numerical calculations for the incoming shock imploding spherically into a diatomic perfect gas. Deviations from the universal solution are extremely small. A solution for the initially infinitesimally weak shock obtained by using Whitham’s (Linear and nonlinear waves, Wiley, New York, 1974) Shock Dynamics is virtually indistinguishable from the Ponchaut solution.
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Ponchaut N.F., Hornung H.G., Pullin D.I., Mouton C.A.: On imploding cylindrical and spherical shock waves in a perfect gas. J. Fluid Mech. 560, 102–122 (2006)
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Dedicated to Professor Wilhelm Schneider on the occasion of his 70th birthday
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Hornung, H.G., Pullin, D.I. & Ponchaut, N.F. On the question of universality of imploding shock waves. Acta Mech 201, 31–35 (2008). https://doi.org/10.1007/s00707-008-0070-2
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DOI: https://doi.org/10.1007/s00707-008-0070-2