2006
DOI: 10.1017/s0022112006000590
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On imploding cylindrical and spherical shock waves in a perfect gas

Abstract: The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law re… Show more

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Cited by 46 publications
(23 citation statements)
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“…A similar calculation using the first equation of (18) gives that the gas velocity immediately behind the shock in the laboratory frame of reference approaches the finite value u → −4 A/3 when r → 0. These results are consistent with (12). Figure 7 illustrates u − c characteristics obtained by integration of the equation dr/dt = u − c using a range of initial conditions and with (u, c) obtained from the numerical solutions.…”
Section: B Comparison Of Numerical Solution With Shock Dynamicssupporting
confidence: 83%
See 1 more Smart Citation
“…A similar calculation using the first equation of (18) gives that the gas velocity immediately behind the shock in the laboratory frame of reference approaches the finite value u → −4 A/3 when r → 0. These results are consistent with (12). Figure 7 illustrates u − c characteristics obtained by integration of the equation dr/dt = u − c using a range of initial conditions and with (u, c) obtained from the numerical solutions.…”
Section: B Comparison Of Numerical Solution With Shock Dynamicssupporting
confidence: 83%
“…11 When applied to the symmetrically converging shock of the Guderley type, GSD provides an extremely accurate approximation to power-law exponents and in fact can describe an almost universal shock collapse process from an infinitesimal wave at infinity to a strong-shock state near the point of convergence. 12,13 Interest in the effect of a magnetic field on the shock convergence process has been heightened by the knowledge that the presence of a sufficiently strong magnetic field can inhibit the RichtmyerMeshkov 14,15 instability that occurs when a shock-wave impacts and impulsively accelerates a perturbed density interface, thereby depositing vorticity and leading to rapid interface growth. 16,17 Suppression of the Richtmyer-Meshkov instability, while retaining the effects of shock heating, could be expected to have potentially important consequences for the realization of inertial confinement fusion (ICF).…”
Section: Introductionmentioning
confidence: 99%
“…But his theory was only valid for strong shocks. Ponchaut et al [13] adopted the method of series expansion and developed a numerical, characteristics based solution which was also valid for weak shocks. In the context of the RMI, Lombardini and Pullin [14] developed the theory for asymptotic growth rate in density interface for a three dimensional cylindrical geometry.…”
Section: Introductionmentioning
confidence: 99%
“…For finite strength shock waves, the approximate theory known as geometric shock dynamics ͑see Ref. 3͒ is most useful, though a more exact solution describing a generalized, "universal" shock implosion has been obtained by Ponchaut et al 5 These authors used various methods including a series expansion solution in which the Guderley solution forms the leadingorder term. This generalized implosion is asymptotic to the Guderley solution ͑in space and time͒ as time increases and the shock strength increases.…”
Section: Introductionmentioning
confidence: 99%