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On the propagation of a multi-dimensional shock of arbitrary strength

Srinivasan, R and Prasad, Phoolan (1985) On the propagation of a multi-dimensional shock of arbitrary strength. In: Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 94 (1). pp. 27-42.

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Abstract

In this paper the kinematics of a curved shock of arbitrary strength has been discussed using the theory of generalised functions. This is the extension of Moslov’s work where he has considered isentropic flow even across the shock. The condition for a nontrivial jump in the flow variables gives the shock manifold equation (sme). An equation for the rate of change of shock strength along the shock rays (defined as the characteristics of the sme) has been obtained. This exact result is then compared with the approximate result of shock dynamics derived by Whitham. The comparison shows that the approximate equations of shock dynamics deviate considerably from the exact equations derived here. In the last section we have derived the conservation form of our shock dynamic equations. These conservation forms would be very useful in numerical computations as it would allow us to derive difference schemes for which it would not be necessary to fit the shock-shock explicitly.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Indian Academy of Sciences.
Keywords: Nonlinear waves;shock dynamics;multi-dimensional shock propagation.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 22 Jan 2010 05:34
Last Modified: 19 Sep 2010 05:43
URI: http://eprints.iisc.ernet.in/id/eprint/22879

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