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Blast Quantification Using Hopkinson Pressure Bars
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Shock waves from the inhomogeneous Boltzmann equation.

Yves Pomeau1, Minh-Binh Tran2

  • 1LadHyX, Laboratoire d'hydrodynamique, Ladhyx, Ecole Polytechnique, 91120 Palaiseau, France.

Physical Review. E
|January 23, 2020
PubMed
Summary

This study corrects self-similar solutions for shock wave structures in gases, ensuring finite energy and physically realistic behavior in kinetic theory. The findings improve models of shock wave inner structures.

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Area of Science:

  • Fluid Dynamics
  • Kinetic Theory
  • Statistical Mechanics

Background:

  • The inner structure of shock waves is modeled using the Boltzmann kinetic equation.
  • Previous self-similar approaches for power-law interactions yielded infinite energy solutions, lacking physical realism.
  • Infinite energy solutions are inconsistent with energy-conserving collisions in gas kinetic theory.

Purpose of the Study:

  • To provide a physically sound correction to self-similar solutions for shock wave structures.
  • To address the issue of infinite energy in existing models.
  • To ensure shock wave perturbations do not unrealistically grow at large distances.

Main Methods:

  • Revisiting the Boltzmann kinetic equation for shock wave inner structure analysis.
  • Focusing on solutions to the spatial homogeneous Boltzmann equation without finite energy.
  • Developing a corrected self-similar form for shock wave solutions.

Main Results:

  • A corrected self-similar form for shock wave solutions is proposed.
  • The corrected solutions exhibit finite energy, enhancing physical realism.
  • The perturbation growth at large distances on the cold side is mitigated in the soft potential case.

Conclusions:

  • The corrected self-similar solutions offer a more physically meaningful description of shock wave inner structures.
  • This work advances the understanding of non-equilibrium gas dynamics.
  • The findings contribute to the rigorous study of Boltzmann equation solutions in kinetic theory.