Global solutions describing the collapse of a spherical or cylindrical cavity

PL, Sachdev and Neelam, Gupta and DS, Ahluwalia (1992) Global solutions describing the collapse of a spherical or cylindrical cavity. In: Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 43 (5). pp. 856-874.

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Abstract

The collapse of a spherical (cylindrical) cavity in air is studied analytically. The global solution for the entire domain between the sound front, separating the undisturbed and the disturbed gas, and the vacuum front is constructed in the form of infinite series in time with coefficients depending on an ldquoappropriaterdquo similarity variable. At timet=0+, the exact planar solution for a uniformly moving cavity is assumed to hold. The global analytic solution of this initial boundary value problem is found until the collapse time (=(gamma–1)/2) for gamma le 1+(2/(1+v)), wherev=1 for cylindrical geometry, andv=2 for spherical geometry. For higher values of gamma, the solution series diverge at timet — 2(beta–1)/ (v(1+beta)+(1–beta)2) where beta=2/(gamma–1). A close agreement is found in the prediction of qualitative features of analytic solution and numerical results of Thomaset al. [1].

Item Type:	Journal Article
Publication:	Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Mar 2011 07:16
Last Modified:	26 Mar 2011 07:16
URI:	http://eprints.iisc.ac.in/id/eprint/36145

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