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arXiv · 2609.30002

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 \(C^1\) 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.

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Qianfeng Li, Meizhi Qian. 2026-09-24. Reconstruction of a Wedge and Post-Shock Flow from a Prescribed Leading Shock. https://arxiv.org/abs/2609.30002

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