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

• Published in: International 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
• Language: English
• 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
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.4285

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.