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Extension of geometrical shock dynamics for blast wave propagation

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Abstract

The direct numerical simulation of blast waves is a challenging task due to the wide range of spatial and temporal scales involved. Moreover, in a real environment (topography, urban area), the blast wave interacts with geometrical obstacles, resulting in reflection, diffraction, and wave recombination phenomena. The shape of the front becomes complex, which limits the efficiency of simple empirical methods. This work aims at contributing to the development of a fast running method for blast waves propagating in the presence of obstacles. This is achieved through an ad hoc extension of the simplified hyperbolic geometrical shock dynamics (GSD) model, which leads to a drastic reduction in the computational cost in comparison with the full Euler system. The new model, called geometrical blast dynamics, is able to take into account any kind of source and obstacle. It relies on a previous extension of GSD for diffraction over wedges to obtain consistent physical behavior, especially in the limit of low Mach numbers. The new model is fully described. Its numerical integration is straightforward. Results compare favorably with experiments, semiempirical models from the literature, and Eulerian simulations, over a wide range of configurations.

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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 Sorbonne University.

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Authors and Affiliations

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

    J. Ridoux & N. Lardjane

  2. Inria, CNRS, LJAD, EPC COFFEE, Université Côte d’Azur, Parc Valrose, 06108, Nice, France

    L. Monasse

  3. UMR 7190 CNRS, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    J. Ridoux & F. Coulouvrat

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  1. J. Ridoux
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Correspondence to N. Lardjane.

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Communicated by C. Needham.

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Appendix: Results for blast wave reflection over a concave corner

Appendix: Results for blast wave reflection over a concave corner

Numerical results for reflection of a spherical blast wave over a concave corner, as explained in Sect. 5.2, are summarized in Table 8. 2D axisymmetric Lagrangian simulations have been performed with \(\Delta s=0.005\) m. For \({\text {dist}}=1\) m and \(\theta _\mathrm {w}=90^\circ \), the shock–shock meets the axis of symmetry resulting in a second Mach stem which perturbs results at 5 m from the corner.

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Ridoux, J., Lardjane, N., Monasse, L. et al. Extension of geometrical shock dynamics for blast wave propagation. Shock Waves 30, 563–583 (2020). https://doi.org/10.1007/s00193-020-00954-z

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