Transonic Solutions for the Mach Reflection of Weak Shocks
We present numerical solutions of the steady and unsteady transonic small disturbance equations that describe the Mach reflection of weak shock waves. The solutions contain a complex structure consisting of a sequence of triple points and tiny supersonic patches directly behind the leading triple point, formed by the reflection of weak shocks and expansion waves between the sonic line and the Mach shock. The presence of an expansion fan at each triple point resolves the von Neumann paradox. The numerical results and theoretical considerations suggest that there may be an infinite sequence of triple points in an inviscid weak shock Mach reflection.
Keywordsvon Neumann paradox weak shock Mach reflection self-similar solutions
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- K. G. Guderley, The Theory of Transonic Flow, Pergamon Press, Oxford, 1962.Google Scholar