NDLI: Strong Convergent Shock Waves Near the Center of Convergence:A Power Series Solution

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hafner, Peter
Copyright Year	1988
Abstract	A Lagrangian formulation of the self-similar convergent shock problem is presented for a quiescent perfect gas of zero pressure. The initial density is either constant or decreasing towards the center according to a power law. One-dimensional plane, cylindrical, or spherical geometry is assumed. The paper is based on a power series representation of the nondimensional flow velocity $f(\tau )$. Density, pressure, and particle trajectories are expressed analytically by f. Similarity parameters $\alpha $, introduced as the near-center limit of a function describing the motion of the shock front, are determined by requiring the power series of f to converge. Defining characteristic polynomials $P_n (\alpha )$ by the derivatives $f^{(n)} (1)$ generated from an ordinary differential equation, $\alpha $ is given by the limiting value of a converging sequence $\{ \alpha _n \| n = 1, \cdots \} $ of real zeros of $P_n (\alpha )$. Similarity parameters $\alpha \approx \alpha _n $ are given to 15 significant decimal digits.
Starting Page	1244
Ending Page	1261
Page Count	18
File Format	PDF
ISSN	00361399
DOI	10.1137/0148076
e-ISSN	1095712X
Issue Number	6
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-10
Access Restriction	Subscribed
Subject Keyword	Gas dynamics, general Lagrangian coordinates Fluid mechanics Partial differential equations gas dynamics Series solutions Nonlinear first-order hyperbolic equations nonlinear eigenvalue problem Shock waves and blast waves convergent shock waves Nonlinear eigenvalue problems, nonlinear spectral theory Shocks and singularities self-similar flow similarity parameters
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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