A finite scale model for shock structure

Margolin, Len G.; Plesko, Catherine Suzanne; Reisner, Jon Michael

doi:10.1016/j.physd.2019.132308

Title: A finite scale model for shock structure

Abstract

In this paper we explore the use of a finite scale model of fluid dynamics to predict the finite structure of a shock wave in a perfect gas. We begin by documenting the history and issues that have arisen when Navier–Stokes theory is applied to the shock structure problem, and continue by motivating the improvement that finite scale theory might provide from its representation of inviscid (anomalous) dissipation. Furthermore, our primary results include the formulation of a traveling wave equation from finite scale theory, an analysis of the solutions of that equation as regards shock width and monotonicity properties, and an estimation of the critical parameter of the theory from experimental data.

Authors:

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2019-12-27

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1581576

Alternate Identifier(s):: OSTI ID: 1693718

Report Number(s):: LA-UR-19-26111
Journal ID: ISSN 0167-2789; TRN: US2101871

Grant/Contract Number:: 89233218CNA000001

Resource Type:: Accepted Manuscript

Journal Name:: Physica. D, Nonlinear Phenomena

Additional Journal Information:: Journal Volume: 403; Journal Issue: C; Journal ID: ISSN 0167-2789

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Margolin, Len G., Plesko, Catherine Suzanne, and Reisner, Jon Michael. A finite scale model for shock structure.  United States: N. p., 2019. 
Web.  doi:10.1016/j.physd.2019.132308.

Copy to clipboard


                    Margolin, Len G., Plesko, Catherine Suzanne, & Reisner, Jon Michael. A finite scale model for shock structure.  United States.  https://doi.org/10.1016/j.physd.2019.132308

Copy to clipboard


                    Margolin, Len G., Plesko, Catherine Suzanne, and Reisner, Jon Michael. Fri .  
"A finite scale model for shock structure".  United States.  https://doi.org/10.1016/j.physd.2019.132308.  https://www.osti.gov/servlets/purl/1581576.

Copy to clipboard


                    
@article{osti_1581576,

  title        = {A finite scale model for shock structure},

  author       = {Margolin, Len G. and Plesko, Catherine Suzanne and Reisner, Jon Michael},

  abstractNote = {In this paper we explore the use of a finite scale model of fluid dynamics to predict the finite structure of a shock wave in a perfect gas. We begin by documenting the history and issues that have arisen when Navier–Stokes theory is applied to the shock structure problem, and continue by motivating the improvement that finite scale theory might provide from its representation of inviscid (anomalous) dissipation. Furthermore, our primary results include the formulation of a traveling wave equation from finite scale theory, an analysis of the solutions of that equation as regards shock width and monotonicity properties, and an estimation of the critical parameter of the theory from experimental data.},

  doi          = {10.1016/j.physd.2019.132308},

  journal      = {Physica. D, Nonlinear Phenomena},

  number       = C,

  volume       = 403,

  place        = {United States},

  year         = {2019},

  month        = {12}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.physd.2019.132308

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 2 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

VonNeumann, J.; Richtmyer, R. D.
Journal of Applied Physics, Vol. 21, Issue 3
DOI: 10.1063/1.1699639

Numerical simulation of turbulent mixing by Rayleigh-Taylor instability
journal, July 1984

Youngs, David L.
Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3
DOI: 10.1016/0167-2789(84)90512-8

Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability
journal, May 1991

Youngs, David L.
Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
DOI: 10.1063/1.858059

Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
journal, December 1994

Youngs, D. L.
Laser and Particle Beams, Vol. 12, Issue 4
DOI: 10.1017/S0263034600008557

Molecular mixing in Rayleigh–Taylor instability
journal, April 1994

Linden, P. F.; Redondo, J. M.; Youngs, D. L.
Journal of Fluid Mechanics, Vol. 265
DOI: 10.1017/S0022112094000777

The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability
journal, May 2010

Thornber, B.; Drikakis, D.; Youngs, D. L.
Journal of Fluid Mechanics, Vol. 654
DOI: 10.1017/S0022112010000492

Modeling of Rayleigh-Taylor mixing using single-fluid models
journal, January 2019

Kokkinakis, Ioannis W.; Drikakis, Dimitris; Youngs, David L.
Physical Review E, Vol. 99, Issue 1
DOI: 10.1103/PhysRevE.99.013104

Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
journal, March 1977

Van Leer, Bram
Journal of Computational Physics, Vol. 23, Issue 3
DOI: 10.1016/0021-9991(77)90095-X

A rationale for implicit turbulence modelling
journal, January 2002

Margolin, Len G.; Rider, William J.
International Journal for Numerical Methods in Fluids, Vol. 39, Issue 9
DOI: 10.1002/fld.331

Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam
journal, April 1976

Alsmeyer, H.
Journal of Fluid Mechanics, Vol. 74, Issue 3
DOI: 10.1017/S0022112076001912

Electron beam density measurements in shock waves in argon
journal, November 1969

Schmidt, B.
Journal of Fluid Mechanics, Vol. 39, Issue 2
DOI: 10.1017/S0022112069002229

Onsager and the theory of hydrodynamic turbulence
journal, January 2006

Eyink, Gregory L.; Sreenivasan, Katepalli R.
Reviews of Modern Physics, Vol. 78, Issue 1
DOI: 10.1103/RevModPhys.78.87

Traveling wave solutions for finite scale equations
journal, October 2012

Margolin, L. G.; Vaughan, D. E.
Mechanics Research Communications, Vol. 45
DOI: 10.1016/j.mechrescom.2012.07.003

A note on finite-scale Navier–Stokes theory: The case of constant viscosity, strictly adiabatic flow
journal, January 2015

Jordan, P. M.; Keiffer, R. S.
Physics Letters A, Vol. 379, Issue 3
DOI: 10.1016/j.physleta.2014.10.033

The curious events leading to the theory of shock waves
journal, June 2007

Salas, Manuel D.
Shock Waves, Vol. 16, Issue 6
DOI: 10.1007/s00193-007-0084-z

Aerial Plane Waves of Finite Amplitude
journal, September 1910

Rayleigh, L.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 84, Issue 570
DOI: 10.1098/rspa.1910.0075

Sto�welle und Detonation
journal, December 1922

Becker, R.
Zeitschrift f�r Physik, Vol. 8, Issue 1
DOI: 10.1007/BF01329605

Note on Becker's Theory of the Shock Front
journal, November 1944

Thomas, L. H.
The Journal of Chemical Physics, Vol. 12, Issue 11
DOI: 10.1063/1.1723889

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas
journal, November 1949

Morduchow, Morris; Libby, Paul A.
Journal of the Aeronautical Sciences, Vol. 16, Issue 11
DOI: 10.2514/8.11882

Entropy in self-similar shock profiles
journal, October 2017

Margolin, L. G.; Reisner, J. M.; Jordan, P. M.
International Journal of Non-Linear Mechanics, Vol. 95
DOI: 10.1016/j.ijnonlinmec.2017.07.003

Beyond the Navier–Stokes equations: Burnett hydrodynamics
journal, August 2008

Garciacolin, L.; Velasco, R.; Uribe, F.
Physics Reports, Vol. 465, Issue 4
DOI: 10.1016/j.physrep.2008.04.010

Modeling shock-wave deformation via molecular dynamics
journal, April 1988

Holian, Brad Lee
Physical Review A, Vol. 37, Issue 7
DOI: 10.1103/PhysRevA.37.2562

One-Dimensional Multiple-Temperature Gas-Kinetic Bhatnagar-Gross-Krook Scheme for Shock Wave Computation
journal, May 2008

Cai, Chunpei; Liu, Danny D.; Xu, Kun
AIAA Journal, Vol. 46, Issue 5
DOI: 10.2514/1.27432

Simulations of Compressible Flows with Strong Shocks by an Adaptive Lattice Boltzmann Model
journal, June 2000

Sun, Chenghai
Journal of Computational Physics, Vol. 161, Issue 1
DOI: 10.1006/jcph.2000.6487

Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent
journal, January 2019

Saadat, Mohammad Hossein; Bösch, Fabian; Karlin, Ilya V.
Physical Review E, Vol. 99, Issue 1
DOI: 10.1103/PhysRevE.99.013306

The Solution of the Boltzmann Equation for a Shock Wave
journal, June 1951

Mott-Smith, H. M.
Physical Review, Vol. 82, Issue 6
DOI: 10.1103/PhysRev.82.885

Computing Turbulent Shear Flows — A Convenient Conspiracy
journal, January 1993

Oran, Elaine S.; Boris, Jay P.
Computers in Physics, Vol. 7, Issue 5
DOI: 10.1063/1.4823213

Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows
journal, June 1994

Porter, D. H.; Pouquet, A.; Woodward, P. R.
Physics of Fluids, Vol. 6, Issue 6
DOI: 10.1063/1.868217

Large-eddy simulations of convective boundary layers using nonoscillatory differencing
journal, September 1999

Margolin, Len G.; Smolarkiewicz, Piotr K.; Sorbjan, Zbigniew
Physica D: Nonlinear Phenomena, Vol. 133, Issue 1-4
DOI: 10.1016/S0167-2789(99)00083-4

Heuristic stability theory for finite-difference equations
journal, June 1968

Hirt, C. W.
Journal of Computational Physics, Vol. 2, Issue 4
DOI: 10.1016/0021-9991(68)90041-7

Finite scale theory: The role of the observer in classical fluid flow
journal, April 2014

Margolin, L. G.
Mechanics Research Communications, Vol. 57
DOI: 10.1016/j.mechrescom.2013.12.004

Finite-scale equations for compressible fluid flow
journal, July 2009

Margolin, L. G.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 367, Issue 1899
DOI: 10.1098/rsta.2008.0290

Discrete regularization
journal, January 2019

Margolin, Len; Plesko, Catherine
Evolution Equations & Control Theory, Vol. 8, Issue 1
DOI: 10.3934/eect.2019007

Conservation laws in discrete geometry
journal, January 2019

G. Margolin, Len; S. Baty, Roy
Journal of Geometric Mechanics, Vol. 11, Issue 2
DOI: 10.3934/jgm.2019010

Structure of a Plane Shock Layer
journal, January 1962

Liepmann, H. W.; Narasimha, R.; Chahine, M. T.
Physics of Fluids, Vol. 5, Issue 11
DOI: 10.1063/1.1706527

The velocity distribution function within a shock wave
journal, November 1967

Bird, G. A.
Journal of Fluid Mechanics, Vol. 30, Issue 3
DOI: 10.1017/S0022112067001557

Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability
journal, August 2015

Gallis, M. A.; Koehler, T. P.; Torczynski, J. R.
Physics of Fluids, Vol. 27, Issue 8
DOI: 10.1063/1.4928338

Use of artificial viscosity in multidimensional fluid dynamic calculations
journal, July 1980

Wilkins, Mark L.
Journal of Computational Physics, Vol. 36, Issue 3
DOI: 10.1016/0021-9991(80)90161-8

A space–time smooth artificial viscosity method for nonlinear conservation laws
journal, February 2013

Reisner, J.; Serencsa, J.; Shkoller, S.
Journal of Computational Physics, Vol. 235
DOI: 10.1016/j.jcp.2012.08.027

Scale matters
journal, March 2018

Margolin, L. G.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2118
DOI: 10.1098/rsta.2017.0235

Similar Records in DOE PAGES and OSTI.GOV collections:

Finite scale theory: Predicting nature’s shocks

Journal Article Margolin, L. G. ; Plesko, C. S. ; Reisner, J. M. - Wave Motion

In this paper, we describe a continuum model that accurately reproduces the experimentally measured structure of physical shocks in a perfect gas. In this work, we begin by presenting a history of shock structure research, theoretical, experimental and numerical, to quantify the significant discrepancies between Navier–Stokes predictions and laboratory measurements. In our first main result, we discuss modifications that generalize the Chapman–Enskog approximation and lead to a new continuum model termed the Finite Scale Equations. In our second main result, we use this continuum model to calculate shock structure with results comparable in accuracy to numerical simulations based on themore » Boltzmann equation.« less
https://doi.org/10.1016/j.wavemoti.2020.102647

Full Text Available
Conservation laws in discrete geometry

Journal Article Margolin, Len G. ; Baty, Roy S. - Journal of Geometric Mechanics

The small length scales of the dissipative processes of physical viscosity and heat conduction are typically not resolved in the numerical simulation of high Reynolds number flows in the discrete geometry of computational grids. Historically, the simulations of flows with shocks and/or turbulence have relied on solving the Euler equations with dissipative regularization. In this paper, we begin by reviewing the regularization strategies used in shock wave calculations in both a Lagrangian and an Eulerian framework. We exhibit the essential similarities with Large Eddy Simulation models of turbulence, namely that almost all of these depend on the square of themore »« less
Cited by 1
https://doi.org/10.3934/jgm.2019010

Full Text Available
Coarse-grained simulations of vortex dynamics and transition in complex high-Re flows

Conference Grinstein, Fernando F

Turbulent flow complexity in applications in engineering, geophysics and astrophysics typically requires achieving accurate and dependable large scale predictions of highly nonlinear processes with under-resolved computer simulation models. Laboratory observations typically demonstrate the end outcome of complex non-linear three-dimensional physical processes with many unexplained details and mechanisms. Carefully controlled computational experiments based on the numerical solution of the conservation equations for mass, momentum, and energy, provide insights into the underlying flow dynamics. Relevant computational fluid dynamics issues to be addressed relate to the modeling of the unresolved tlow conditions at the subgrid scale (SGS) level - within a computational cell,more »« less
Full Text Available
Numerical study of heterogeneous mean temperature and shock wave in a resonator

Journal Article Yano, Takeru - AIP Conference Proceedings

When a frequency of gas oscillation in an acoustic resonator is sufficiently close to one of resonant frequencies of the resonator, the amplitude of gas oscillation becomes large and hence the nonlinear effect manifests itself. Then, if the dissipation effects due to viscosity and thermal conductivity of the gas are sufficiently small, the gas oscillation may evolve into the acoustic shock wave, in the so-called consonant resonators. At the shock front, the kinetic energy of gas oscillation is converted into heat by the dissipation process inside the shock layer, and therefore the temperature of the gas in the resonator rises.more »« less
https://doi.org/10.1063/1.4934437
Theoretical and numerical structure for reacting shock waves

Journal Article Colella, P ; Majda, A ; Roytburd, V - SIAM J. Sci. Stat. Comput.; (United States)

Several remarkable theoretical and computational properties of reacting shock waves are both documented and analyzed. In particular, for sufficiently small heat release or large reaction rate, the authors demonstrate that the reacting compressible Navier-Stokes equations have dynamically stable weak detonations which occur in bifurcating wave patterns from strong detonation initial data. In the reported calculations, an increase in reaction rate by a factor of 5 is sufficient to create the bifurcation from a spiked nearly Z-N-D detonation to the wave pattern with a precursor weak detonation. The numerical schemes used in the calculations are fractional step methods based on themore »« less
https://doi.org/10.1137/0907073

Similar Records

Title: A finite scale model for shock structure

Abstract

Citation Formats

A Method for the Numerical Calculation of Hydrodynamic Shocks journal, March 1950

Numerical simulation of turbulent mixing by Rayleigh-Taylor instability journal, July 1984

Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability journal, May 1991

Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities journal, December 1994

Molecular mixing in Rayleigh–Taylor instability journal, April 1994

The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability journal, May 2010

Modeling of Rayleigh-Taylor mixing using single-fluid models journal, January 2019

Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection journal, March 1977

A rationale for implicit turbulence modelling journal, January 2002

Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam journal, April 1976

Electron beam density measurements in shock waves in argon journal, November 1969

Onsager and the theory of hydrodynamic turbulence journal, January 2006

Traveling wave solutions for finite scale equations journal, October 2012

A note on finite-scale Navier–Stokes theory: The case of constant viscosity, strictly adiabatic flow journal, January 2015

The curious events leading to the theory of shock waves journal, June 2007

Aerial Plane Waves of Finite Amplitude journal, September 1910

Sto�welle und Detonation journal, December 1922

Note on Becker's Theory of the Shock Front journal, November 1944

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas journal, November 1949

Entropy in self-similar shock profiles journal, October 2017

Beyond the Navier–Stokes equations: Burnett hydrodynamics journal, August 2008

Modeling shock-wave deformation via molecular dynamics journal, April 1988

One-Dimensional Multiple-Temperature Gas-Kinetic Bhatnagar-Gross-Krook Scheme for Shock Wave Computation journal, May 2008

Simulations of Compressible Flows with Strong Shocks by an Adaptive Lattice Boltzmann Model journal, June 2000

Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent journal, January 2019

The Solution of the Boltzmann Equation for a Shock Wave journal, June 1951

Computing Turbulent Shear Flows — A Convenient Conspiracy journal, January 1993

Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows journal, June 1994

Large-eddy simulations of convective boundary layers using nonoscillatory differencing journal, September 1999

Heuristic stability theory for finite-difference equations journal, June 1968

Finite scale theory: The role of the observer in classical fluid flow journal, April 2014

Finite-scale equations for compressible fluid flow journal, July 2009

Discrete regularization journal, January 2019

Conservation laws in discrete geometry journal, January 2019

Structure of a Plane Shock Layer journal, January 1962

The velocity distribution function within a shock wave journal, November 1967

Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability journal, August 2015

Use of artificial viscosity in multidimensional fluid dynamic calculations journal, July 1980

A space–time smooth artificial viscosity method for nonlinear conservation laws journal, February 2013

Scale matters journal, March 2018

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

Numerical simulation of turbulent mixing by Rayleigh-Taylor instability
journal, July 1984

Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability
journal, May 1991

Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
journal, December 1994

Molecular mixing in Rayleigh–Taylor instability
journal, April 1994

The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability
journal, May 2010

Modeling of Rayleigh-Taylor mixing using single-fluid models
journal, January 2019

Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
journal, March 1977

A rationale for implicit turbulence modelling
journal, January 2002

Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam
journal, April 1976

Electron beam density measurements in shock waves in argon
journal, November 1969

Onsager and the theory of hydrodynamic turbulence
journal, January 2006

Traveling wave solutions for finite scale equations
journal, October 2012

A note on finite-scale Navier–Stokes theory: The case of constant viscosity, strictly adiabatic flow
journal, January 2015

The curious events leading to the theory of shock waves
journal, June 2007

Aerial Plane Waves of Finite Amplitude
journal, September 1910

Sto�welle und Detonation
journal, December 1922

Note on Becker's Theory of the Shock Front
journal, November 1944

On a Complete Solution of the One-Dimensional Flow Equations of a Viscous, Heat-Conducting, Compressible Gas
journal, November 1949

Entropy in self-similar shock profiles
journal, October 2017

Beyond the Navier–Stokes equations: Burnett hydrodynamics
journal, August 2008

Modeling shock-wave deformation via molecular dynamics
journal, April 1988

One-Dimensional Multiple-Temperature Gas-Kinetic Bhatnagar-Gross-Krook Scheme for Shock Wave Computation
journal, May 2008

Simulations of Compressible Flows with Strong Shocks by an Adaptive Lattice Boltzmann Model
journal, June 2000

Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent
journal, January 2019

The Solution of the Boltzmann Equation for a Shock Wave
journal, June 1951

Computing Turbulent Shear Flows — A Convenient Conspiracy
journal, January 1993

Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows
journal, June 1994

Large-eddy simulations of convective boundary layers using nonoscillatory differencing
journal, September 1999

Heuristic stability theory for finite-difference equations
journal, June 1968

Finite scale theory: The role of the observer in classical fluid flow
journal, April 2014

Finite-scale equations for compressible fluid flow
journal, July 2009

Discrete regularization
journal, January 2019

Conservation laws in discrete geometry
journal, January 2019

Structure of a Plane Shock Layer
journal, January 1962

The velocity distribution function within a shock wave
journal, November 1967

Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability
journal, August 2015

Use of artificial viscosity in multidimensional fluid dynamic calculations
journal, July 1980

A space–time smooth artificial viscosity method for nonlinear conservation laws
journal, February 2013

Scale matters
journal, March 2018