Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Kinematics of a shock wave of arbitrary strength in a non-ideal gas

Authors: Manoj Pandey and V. D. Sharma
Journal: Quart. Appl. Math. 67 (2009), 401-418
MSC (2000): Primary 35L50, 35L67, 35L65, 76L05
DOI: https://doi.org/10.1090/S0033-569X-09-01111-5
Published electronically: May 5, 2009
MathSciNet review: 2547633
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Abstract | References | Similar Articles | Additional Information

Abstract: Singular surface theory is used to study the evolutionary behaviour of an unsteady three-dimensional motion of a shock wave of arbitrary strength propagating through a non-ideal gas. The dynamical coupling between the shock front and the induced discontinuities behind it is investigated by considering an infinite system of transport equations governing the strength of a shock wave and the induced discontinuities behind it. This infinite system, when subjected to a truncation approximation, efficiently describes the shock motion. Disturbances propagating on the shock and the onset of shock-shocks are briefly discussed. For a two-dimensional shock motion, our transport equations bear a structural resemblance to those of geometrical shock dynamics. Attention is drawn to the connection between the transport equation obtained by using the truncation rule and the one obtained by using the characteristic rule. The effects of van der Waals' excluded volume and wavefront geometry on the evolutionary behaviour of shocks are discussed.

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Additional Information

Manoj Pandey
Affiliation: Department of Mathematics, I.I.T. Bombay, Powai Mumbai, India 400076
Email: mkp@math.iitb.ac.in

V. D. Sharma
Affiliation: Department of Mathematics, I.I.T. Bombay, Powai Mumbai, India 400076
Email: vsharma@maths.iitb.ac.in

DOI: https://doi.org/10.1090/S0033-569X-09-01111-5
Keywords: Singular surface theory, non-ideal gas, shock wave, geometrical shock dynamics
Received by editor(s): March 21, 2007
Published electronically: May 5, 2009
Additional Notes: Research support from ISRO-IIT Bombay, Space Technology Cell (Ref. No. 05-IS001) is gratefully acknowledged.
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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