Numerical simulation of cylindrical solitary waves in periodic media

Citation data:

Journal of Scientific Computing, ISSN: 0885-7474, Vol: 58, Issue: 3, Page: 672-689

Publication Year:
2014
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arXiv Id:
1209.5164
DOI:
10.1007/s10915-013-9747-3
Repository URL:
http://hdl.handle.net/10754/333581; http://arxiv.org/abs/1209.5164
Author(s):
Quezada de Luna, Manuel; Ketcheson, David I.
Publisher(s):
Springer Nature; Springer Verlag
Tags:
Mathematics; Computer Science; Engineering; Stegotons; Solitary waves; Periodic media; Effective dispersion; Hyperbolic PDEs; Riemann solvers; Mathematics - Numerical Analysis; Condensed Matter - Materials Science
article description
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion. © Springer Science+Business Media New York 2013.