The Guderley problem revisited
Abstract
The selfsimilar convergingdiverging shock wave problem introduced by Guderley in 1942 has been the source of numerous investigations since its publication. In this paper, we review the simplifications and group invariance properties that lead to a selfsimilar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the selfsimilar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the socalled similarity exponent for the converging flow, and that of the second is a trajectory multiplier for the diverging regime. We provide a clear exposition concerning the reflected shock configuration. Additionally, we introduce a new approximation for the similarity exponent, which we compare with other estimates and numerically computed values. Lastly, we use the Guderley problem as the basis of a quantitative verification analysis of a cellcentered, finite volume, Eulerian compressible flow algorithm.
 Authors:
 Los Alamos National Laboratory
 NON LANL
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 970025
 Report Number(s):
 LAUR0905853; LAUR095853
TRN: US1000718
 DOE Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Shock Waves
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75; APPROXIMATIONS; COMPRESSIBLE FLOW; CONFIGURATION; EIGENVALUES; SHOCK WAVES; VERIFICATION
Citation Formats
Ramsey, Scott D, Kamm, James R, and Bolstad, John H. The Guderley problem revisited. United States: N. p., 2009.
Web.
Ramsey, Scott D, Kamm, James R, & Bolstad, John H. The Guderley problem revisited. United States.
Ramsey, Scott D, Kamm, James R, and Bolstad, John H. Thu .
"The Guderley problem revisited". United States.
doi:. https://www.osti.gov/servlets/purl/970025.
@article{osti_970025,
title = {The Guderley problem revisited},
author = {Ramsey, Scott D and Kamm, James R and Bolstad, John H},
abstractNote = {The selfsimilar convergingdiverging shock wave problem introduced by Guderley in 1942 has been the source of numerous investigations since its publication. In this paper, we review the simplifications and group invariance properties that lead to a selfsimilar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the selfsimilar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the socalled similarity exponent for the converging flow, and that of the second is a trajectory multiplier for the diverging regime. We provide a clear exposition concerning the reflected shock configuration. Additionally, we introduce a new approximation for the similarity exponent, which we compare with other estimates and numerically computed values. Lastly, we use the Guderley problem as the basis of a quantitative verification analysis of a cellcentered, finite volume, Eulerian compressible flow algorithm.},
doi = {},
journal = {Shock Waves},
number = ,
volume = ,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2009},
month = {Thu Jan 01 00:00:00 EST 2009}
}

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