Global solutions describing the collapse of a spherical or cylindrical cavity

Document Type

Article

Publication Date

9-1-1992

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 "appropriate" similarity variable. At time t=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 (=(γ-1)/2) for γ ≤ 1+(2/(1+v)), where v=1 for cylindrical geometry, and v=2 for spherical geometry. For higher values of γ, the solution series diverge at time t - 2(β-1)/ (v(1+β)+(1-β)2) where β=2/(γ-1). A close agreement is found in the prediction of qualitative features of analytic solution and numerical results of Thomas et al. [1]. © 1992 Birkhäuser Verlag.

Identifier

34249834506 (Scopus)

Publication Title

ZAMP Zeitschrift Fur Angewandte Mathematik Und Physik

External Full Text Location

https://doi.org/10.1007/BF00913411

e-ISSN

14209039

ISSN

00442275

First Page

856

Last Page

874

Issue

5

Volume

43

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