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Title: The Guderley problem revisited

Abstract

The self-similar converging-diverging 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 self-similar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the self-similar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the so-called 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 cell-centered, finite volume, Eulerian compressible flow algorithm.

Authors:
 [1];  [1];  [2]
  1. Los Alamos National Laboratory
  2. 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):
LA-UR-09-05853; LA-UR-09-5853
TRN: US1000718
DOE Contract Number:
AC52-06NA25396
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 self-similar converging-diverging 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 self-similar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the self-similar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the so-called 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 cell-centered, 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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