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Uniformly valid analytical solution to the problem of a decaying shock wave

Published online by Cambridge University Press:  21 April 2006

V. D. Sharma
Affiliation:
Department of Applied Mathematics, Institute of Technology, B.H.U., Varanasi 221005, India
Rishi Ram
Affiliation:
Department of Applied Mathematics, Institute of Technology, B.H.U., Varanasi 221005, India
P. L. Sachdev
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India

Abstract

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Type
Research Article
Copyright
© 1987 Cambridge University Press

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References

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