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Shock wave focusing using geometrical shock dynamics

Cates, J. E. and Sturtevant, B. (1997) Shock wave focusing using geometrical shock dynamics. Physics of Fluids, 9 (10). pp. 3058-3068. ISSN 1070-6631. doi:10.1063/1.869414.

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A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The numerical results exhibit the qualitative behavior of strong, moderate, and weak shock focusing observed experimentally. The physical mechanisms that are influenced by aperture angle and shock strength are properly represented by geometrical shock dynamics. Comparison with experimental measurements of the location at which maximum shock pressure occurs shows good agreement, but the maximum pressure at focus is overestimated by about 60%. This error, though large, is acceptable when the speed and low cost of the method is taken into consideration. The error is primarily due to the under prediction of disturbance speed on weak shock fronts. Adequate resolution of the focal region proves to be particularly important to properly judge the validity of shock dynamics theory, under-resolution leading to overly optimistic conclusions.

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Additional Information:©1997 American Institute of Physics. (Received 7 January 1997; accepted 23 April 1997) This work was supported by the NIDDK, National Institutes of Health under Grant No. P01 DK43881-01A3 and, in part, by a National Science Foundation Fellowship.
Subject Keywords:shock waves; focusing; finite difference methods; nonlinear equations
Issue or Number:10
Record Number:CaltechAUTHORS:CATpof97
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2069
Deposited By: Archive Administrator
Deposited On:06 Mar 2006
Last Modified:08 Nov 2021 19:44

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