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On methods of calculating successive positions of a shock front

Prasad, P and Srinivasan, R (1988) On methods of calculating successive positions of a shock front. In: Acta Mechanica, 74 (1-4). pp. 81-93.

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In this paper we have discussed limits of the validity of Whitham's characteristic rule for finding successive positions of a shock in one space dimension. We start with an example for which the exact solution is known and show that the characteristic rule gives correct result only if the state behind the shock is uniform. Then we take the gas dynamic equations in two cases: one of a shock propagating through a stratified layer and other down a nonuniform tube and derive exact equations for the evolution of the shock amplitude along a shock path. These exact results are then compared with the results obtained by the characteristic rule. The characteristic rule not only incorrectly accounts for the deviation of the state behind the shock from a uniform state but also gives a coefficient in the equation which differ significantly from the exact coefficients for a wide range of values of the shock strength.

Item Type: Journal Article
Publication: Acta Mechanica
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Sep 2010 10:07
Last Modified: 24 Sep 2010 10:07
URI: http://eprints.iisc.ac.in/id/eprint/32431

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