Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations

J. W. Lee, Won Suk Ohm, W. Shim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.

Original languageEnglish
Title of host publicationRecent Developments in Nonlinear Acoustics
Subtitle of host publication20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum
EditorsVictor W. Sparrow, Didier Dragna, Philippe Blanc-Benon
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413320
DOIs
Publication statusPublished - 2015 Oct 28
Event20th International Symposium on Nonlinear Acoustics, ISNA 2015, including the 2nd International Sonic Boom Forum, ISBF 2015 - Ecully, Lyon, France
Duration: 2015 Jun 292015 Jul 3

Publication series

NameAIP Conference Proceedings
Volume1685
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other20th International Symposium on Nonlinear Acoustics, ISNA 2015, including the 2nd International Sonic Boom Forum, ISBF 2015
CountryFrance
CityEcully, Lyon
Period15/6/2915/7/3

Fingerprint

wave propagation
shock
Rankine-Hugoniot relation
Cauchy problem
rarefaction
Burger equation
blasts
shock waves
waveforms
hydrodynamics
physics
propagation
fluids
approximation

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Lee, J. W., Ohm, W. S., & Shim, W. (2015). Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations. In V. W. Sparrow, D. Dragna, & P. Blanc-Benon (Eds.), Recent Developments in Nonlinear Acoustics: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum [070011] (AIP Conference Proceedings; Vol. 1685). American Institute of Physics Inc.. https://doi.org/10.1063/1.4934448
Lee, J. W. ; Ohm, Won Suk ; Shim, W. / Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations. Recent Developments in Nonlinear Acoustics: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. editor / Victor W. Sparrow ; Didier Dragna ; Philippe Blanc-Benon. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).
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abstract = "This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.",
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Lee, JW, Ohm, WS & Shim, W 2015, Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations. in VW Sparrow, D Dragna & P Blanc-Benon (eds), Recent Developments in Nonlinear Acoustics: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum., 070011, AIP Conference Proceedings, vol. 1685, American Institute of Physics Inc., 20th International Symposium on Nonlinear Acoustics, ISNA 2015, including the 2nd International Sonic Boom Forum, ISBF 2015, Ecully, Lyon, France, 15/6/29. https://doi.org/10.1063/1.4934448

Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations. / Lee, J. W.; Ohm, Won Suk; Shim, W.

Recent Developments in Nonlinear Acoustics: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. ed. / Victor W. Sparrow; Didier Dragna; Philippe Blanc-Benon. American Institute of Physics Inc., 2015. 070011 (AIP Conference Proceedings; Vol. 1685).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.

AB - This paper presents a computational scheme solely based on the Rankine-Hugoniot shock relations to describe the propagation of strongly-nonlinear waves in fluids, the amplitude of which is so great that second-order approximations such as the weak shock theory and the Burgers equation do not apply. The Rankine-Hugoniot relations are three algebraic equations connecting the flow variables (pressure, density, particle velocity, and energy) across a shock. What is not well known is that the Rankine-Hugoniot relations can be used to compute the nonlinear evolution of the continuous segment of a wave, if the continuous segment can be approximated by a succession of infinitesimal compression shocks [Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002), pp. 85-86]. We further extend this idea to the other continuous segment that can be discretized into a series of infinitesimal rarefaction shocks. The discretization of a waveform and the subsequent application of the Rankine-Hugoniot relations lead to a Riemann problem that conveniently treats continuous segments and real shocks in the same manner. Our computational scheme distinguishes itself from the conventional Riemann problem in that shocks are treated as particles, which facilitates an enormous saving in computation time. The scheme is verified against the 1-D Riemann solver for the case of strong blast waves.

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Lee JW, Ohm WS, Shim W. Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations. In Sparrow VW, Dragna D, Blanc-Benon P, editors, Recent Developments in Nonlinear Acoustics: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. American Institute of Physics Inc. 2015. 070011. (AIP Conference Proceedings). https://doi.org/10.1063/1.4934448