Sanderson, S. R. (2004) Gasdynamic wave interaction in two spatial dimensions. Journal of Fluid Mechanics, 506 . pp. 187-205. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:SANjfm04b
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We examine the interaction of shock waves by studying solutions of the two-dimensional Euler equations about a point. The problem is reduced to linear form by considering local solutions that are constant along each ray and thereby exhibit no length scale at the intersection point. Closed-form solutions are obtained in a unified manner for standard gasdynamics problems including oblique shock waves, Prandtl–Meyer flow and Mach reflection. These canonical gas dynamical problems are shown to reduce to a series of geometrical transformations involving anisotropic coordinate stretching and rotation operations. An entropy condition and a requirement for geometric regularity of the intersection of the incident waves are used to eliminate spurious solutions. Consideration of the downstream boundary conditions leads to a formal determination of the allowable downstream matching criteria. By retaining the time-dependent terms, an approach is suggested for future investigation of the open problem of the stability of shock wave interactions.
|Additional Information:||Copyright © 2004 Cambridge University Press. Reprinted with permission. (Received 6 March 2003 and in revised form 20 November 2003) Published online 28 April 2004. The author is grateful for assistance received from the Darryl G. Greenamyer Fellowship and C.L. Powell Fellowship funds. This work was supported by AFOSR Grant Nos. F49620-92-J-0110 and F49620-93-1-0338.|
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|Deposited On:||25 Sep 2007|
|Last Modified:||26 Dec 2012 09:43|
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