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Reconstruction of a Wedge and Post-Shock Flow from a Prescribed Leading Shock

  • Qianfeng Li
  • Meizhi Qian
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Abstract

In this paper, we reconstruct a wedge and its post-shock flow from a prescribed leading shock and a uniform supersonic incoming state. Full Euler Rankine--Hugoniot relations supply the shock data, while a reduced interior model combines homogeneous acoustic characteristic equations, entropy transport, and the Bernoulli relation. A hodograph transformation yields a linear hyperbolic equation for the physical coordinate. Comparing a shock-to-wedge mass bound with a hodograph non-degeneracy threshold gives a sufficient, data-dependent reconstruction criterion. Under the stated assumptions, this criterion ensures a unique C1 post-shock flow and a C2 wedge throughout the characteristic domain determined by the prescribed shock segment. Numerical reconstructions examine empirical grid convergence, Mach-number dependence, and discrepancies between the reduced-model and full-Euler inverse reconstructions.

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Cite

BibTeXRIS
BibTeX
@misc{li2026reconstruction,
  title = {{Reconstruction of a Wedge and Post-Shock Flow from a Prescribed Leading Shock}},
  author = {Qianfeng Li and Meizhi Qian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30002},
  eprint = {2609.30002},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30002},
}
RIS
TY  - UNPB
TI  - Reconstruction of a Wedge and Post-Shock Flow from a Prescribed Leading Shock
AU  - Qianfeng Li
AU  - Meizhi Qian
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.30002
UR  - https://arxiv.org/abs/2609.30002
AB  - In this paper, we reconstruct a wedge and its post-shock flow from a prescribed leading shock and a uniform supersonic incoming state. Full Euler Rankine--Hugoniot relations supply the shock data, while a reduced interior model combines homogeneous acoustic characteristic equations, entropy transport, and the Bernoulli relation. A hodograph transformation yields a linear hyperbolic equation for the physical coordinate. Comparing a shock-to-wedge mass bound with a hodograph non-degeneracy threshold gives a sufficient, data-dependent reconstruction criterion. Under the stated assumptions, this criterion ensures a unique C^1 post-shock flow and a C^2 wedge throughout the characteristic domain determined by the prescribed shock segment. Numerical reconstructions examine empirical grid convergence, Mach-number dependence, and discrepancies between the reduced-model and full-Euler inverse reconstructions.
ER  -