Regular reflection in self-similar potential flow and the sonic criterion

2007/09/30 by Elling, Volker
#75M10 #76H05 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0710.0104

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 and isentropic coefficients, a solution exists for all wedge angles allowed by the sonic criterion. This demonstrates that, at least for potential flow, weaker criteria are false.

Related

• Instability of strong regular reflection and counterexamples to the detachment criterion
• Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow
• Loss of Regularity of Solutions to Shock Reflection Problems by a Non-symmetric Convex Wedge with Potential Flow Equations
• Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow
• Non-existence of strong regular reflections in self-similar potential flow