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Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation

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Abstract

Geometrical shock dynamics (GSD) is a simplified model for nonlinear shock-wave propagation, based on the decomposition of the shock front into elementary ray tubes. Assuming small changes in the ray tube area, and neglecting the effect of the post-shock flow, a simple relation linking the local curvature and velocity of the front, known as the \(A{-}M\) rule, is obtained. More recently, a new simplified model, referred to as the kinematic model, was proposed. This model is obtained by combining the three-dimensional Euler equations and the Rankine–Hugoniot relations at the front, which leads to an equation for the normal variation of the shock Mach number at the wave front. In the same way as GSD, the kinematic model is closed by neglecting the post-shock flow effects. Although each model’s approach is different, we prove their structural equivalence: the kinematic model can be rewritten under the form of GSD with a specific \(A{-}M\) relation. Both models are then compared through a wide variety of examples including experimental data or Eulerian simulation results when available. Attention is drawn to the simple cases of compression ramps and diffraction over convex corners. The analysis is completed by the more complex cases of the diffraction over a cylinder, a sphere, a mound, and a trough.

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Acknowledgements

Part of this work has been possible thanks to the LETMA collaboration: a contractual research laboratory between CEA, CNRS, École Centrale Lyon, C-Innov, and Université Pierre et Marie Curie. O. Gainville is acknowledged for valuable discussions. We also thank an anonymous reviewer who helped us to improve the quality of this paper.

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Authors and Affiliations

  1. CEA, DAM, DIF, F-91297, Arpajon, France

    J. Ridoux & N. Lardjane

  2. CERMICS, ENPC, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455, Marne la Vallée Cedex 2, France

    L. Monasse

  3. CNRS, Institut Jean Le Rond d’Alembert, UMR 7190, Université Pierre et Marie Curie, Paris 06, Sorbonne Universités, Paris, France

    J. Ridoux & F. Coulouvrat

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  1. J. Ridoux
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  2. N. Lardjane
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Correspondence to N. Lardjane.

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Communicated by A. Hadjadj and A. Higgins.

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Ridoux, J., Lardjane, N., Monasse, L. et al. Comparison of geometrical shock dynamics and kinematic models for shock-wave propagation. Shock Waves 28, 401–416 (2018). https://doi.org/10.1007/s00193-017-0748-2

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