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Regular Reflection in Self-similar Potential Flow and the Sonic Criterion

Commun. Math. Anal.
Volume 8, Number 2 (2010), 22 - 69

Regular Reflection in Self-similar Potential Flow and the Sonic Criterion

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Abstract

Reflection of a shock from a solid wedge is a classical problem in gas dynamics. Depending on the parameters either a regular or a irregular (Mach-type) reflection results. We construct regular reflection as an exact self-similar solution for potential flow. For some upstream Mach numbers MI and isentropic coefficients γ, a solution exists for all wedge angles θ allowed by the sonic criterion. This demonstrates that, at least for potential flow, weaker criteria are false.