A method for computation of discontinuous wave propagation in heterogeneous solids: basic algorithm description and application to one-dimensional problems

SUMMARY An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combi...

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Published inInternational journal for numerical methods in engineering Vol. 91; no. 6; pp. 622 - 643
Main Authors Park, K. C., Lim, S. J, Huh, H.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 10.08.2012
Wiley
Subjects
Engineering Sciences
Exact sciences and technology
explicit integrator
Fundamental areas of phenomenology (including applications)
heterogeneous bar
Mechanics
minimal spurious oscillations
Physics
propagation of stress waves
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Performance evaluation
Numerical integration
minimal spurious oscillations
Stress wave
Elastic wave
explicit integrator
Modeling
Shock front
Wavefront
propagation of stress waves
Strain wave
Filter
heterogeneous bar
Finite difference method
Online AccessGet full text
ISSN0029-5981
1097-0207
1097-0207
DOI10.1002/nme.4285

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Abstract SUMMARY An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward–pullback operations in time designed to filter post‐shock oscillations, and the central difference method that intrinsically filters front‐shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front‐shock and post‐shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars. Copyright © 2012 John Wiley & Sons, Ltd.
AbstractList An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward–pullback operations in time designed to filter post‐shock oscillations, and the central difference method that intrinsically filters front‐shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front‐shock and post‐shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars. Copyright © 2012 John Wiley & Sons, Ltd.
SUMMARY An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward–pullback operations in time designed to filter post‐shock oscillations, and the central difference method that intrinsically filters front‐shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front‐shock and post‐shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars. Copyright © 2012 John Wiley & Sons, Ltd.
An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward–pullback operations in time designed to filter post-shock oscillations, and the central difference method that intrinsically filters front-shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front-shock and post-shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars.
Author Huh, H.
Park, K. C.
Lim, S. J
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Issue 6
Keywords Performance evaluation
Numerical integration
minimal spurious oscillations
Stress wave
Elastic wave
explicit integrator
Modeling
Shock front
Wavefront
propagation of stress waves
Strain wave
Filter
heterogeneous bar
Finite difference method
Language English
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References_xml – reference: Hulbert GM, Hughes TRJ. Space-time finite element methods for second-order hyperbolic equations. Computer Methods in Applied Mechanics and Engineering 1990; 84:327-347.
– reference: Leveque RJ, Shyue KM. Two-dimensional front tracking based on high resolution wave propagation methods. Journal of Computational Physics 1996; 123:354-361.
– reference: Park KC, Underwood PG. A variable-step central difference method for structural dynamic analysis, I: theoretical aspects. Computer Methods in Applied Mechanics and Engineering 1980; 22:241-258.
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Snippet SUMMARY An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing...
An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing...
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SubjectTerms Engineering Sciences
Exact sciences and technology
explicit integrator
Fundamental areas of phenomenology (including applications)
heterogeneous bar
Mechanics
minimal spurious oscillations
Physics
propagation of stress waves
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Title A method for computation of discontinuous wave propagation in heterogeneous solids: basic algorithm description and application to one-dimensional problems
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