Numerical simulation of cylindrically converging shock waves

H. Matsuo, Yuji Ohya, K. Fujiwara, H. Kudoh

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The converging shock wave is assumed to be generated by an instantaneous energy release on a rigid cylindrical wall. The fluid flow caused by its propagation is numerically simulated. The behavior of the solution in the focusing stage is closely investigated and compared with the selfsimilar solution. Results include new details of the transition of the solution from the nonselfsimilar region to the selfsimilar region. Numerical methods such as the random choice method, the method of characteristics, and the second-order accurate finite difference method with artificial viscosities are adopted. The results are also compared with those of the method of integral relations. They all agreed well with one another except for the focusing stage. The random choice method and the method of characteristics produce nearly identical results in the focusing stage, suggesting the mutual credibility of the two methods. Artificial viscosities involved in the finite difference scheme smear out the shock front as it approaches the axis. The comparison with the selfsimilar solution is then difficult.

Original languageEnglish
Pages (from-to)384-399
Number of pages16
JournalJournal of Computational Physics
Volume75
Issue number2
DOIs
Publication statusPublished - Jan 1 1988

Fingerprint

Shock waves
shock waves
method of characteristics
Computer simulation
simulation
Viscosity
viscosity
smear
shock fronts
Finite difference method
fluid flow
Flow of fluids
Numerical methods
propagation
energy

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical simulation of cylindrically converging shock waves. / Matsuo, H.; Ohya, Yuji; Fujiwara, K.; Kudoh, H.

In: Journal of Computational Physics, Vol. 75, No. 2, 01.01.1988, p. 384-399.

Research output: Contribution to journalArticle

Matsuo, H. ; Ohya, Yuji ; Fujiwara, K. ; Kudoh, H. / Numerical simulation of cylindrically converging shock waves. In: Journal of Computational Physics. 1988 ; Vol. 75, No. 2. pp. 384-399.
@article{18cbe4b8d29d4164b341c4f0388c2680,
title = "Numerical simulation of cylindrically converging shock waves",
abstract = "The converging shock wave is assumed to be generated by an instantaneous energy release on a rigid cylindrical wall. The fluid flow caused by its propagation is numerically simulated. The behavior of the solution in the focusing stage is closely investigated and compared with the selfsimilar solution. Results include new details of the transition of the solution from the nonselfsimilar region to the selfsimilar region. Numerical methods such as the random choice method, the method of characteristics, and the second-order accurate finite difference method with artificial viscosities are adopted. The results are also compared with those of the method of integral relations. They all agreed well with one another except for the focusing stage. The random choice method and the method of characteristics produce nearly identical results in the focusing stage, suggesting the mutual credibility of the two methods. Artificial viscosities involved in the finite difference scheme smear out the shock front as it approaches the axis. The comparison with the selfsimilar solution is then difficult.",
author = "H. Matsuo and Yuji Ohya and K. Fujiwara and H. Kudoh",
year = "1988",
month = "1",
day = "1",
doi = "10.1016/0021-9991(88)90119-2",
language = "English",
volume = "75",
pages = "384--399",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Numerical simulation of cylindrically converging shock waves

AU - Matsuo, H.

AU - Ohya, Yuji

AU - Fujiwara, K.

AU - Kudoh, H.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - The converging shock wave is assumed to be generated by an instantaneous energy release on a rigid cylindrical wall. The fluid flow caused by its propagation is numerically simulated. The behavior of the solution in the focusing stage is closely investigated and compared with the selfsimilar solution. Results include new details of the transition of the solution from the nonselfsimilar region to the selfsimilar region. Numerical methods such as the random choice method, the method of characteristics, and the second-order accurate finite difference method with artificial viscosities are adopted. The results are also compared with those of the method of integral relations. They all agreed well with one another except for the focusing stage. The random choice method and the method of characteristics produce nearly identical results in the focusing stage, suggesting the mutual credibility of the two methods. Artificial viscosities involved in the finite difference scheme smear out the shock front as it approaches the axis. The comparison with the selfsimilar solution is then difficult.

AB - The converging shock wave is assumed to be generated by an instantaneous energy release on a rigid cylindrical wall. The fluid flow caused by its propagation is numerically simulated. The behavior of the solution in the focusing stage is closely investigated and compared with the selfsimilar solution. Results include new details of the transition of the solution from the nonselfsimilar region to the selfsimilar region. Numerical methods such as the random choice method, the method of characteristics, and the second-order accurate finite difference method with artificial viscosities are adopted. The results are also compared with those of the method of integral relations. They all agreed well with one another except for the focusing stage. The random choice method and the method of characteristics produce nearly identical results in the focusing stage, suggesting the mutual credibility of the two methods. Artificial viscosities involved in the finite difference scheme smear out the shock front as it approaches the axis. The comparison with the selfsimilar solution is then difficult.

UR - http://www.scopus.com/inward/record.url?scp=5844377989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5844377989&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(88)90119-2

DO - 10.1016/0021-9991(88)90119-2

M3 - Article

AN - SCOPUS:5844377989

VL - 75

SP - 384

EP - 399

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -