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    Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

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    2014_cylindrical_solitary_waves_postprint.pdf
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    Type
    Article
    Authors
    Quezada de Luna, Manuel
    Ketcheson, David I. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Mathematics Group
    Date
    2013-07-14
    Online Publication Date
    2013-07-14
    Print Publication Date
    2014-03
    Permanent link to this record
    http://hdl.handle.net/10754/333581
    
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    Abstract
    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.
    Citation
    Numerical Simulation of Cylindrical Solitary Waves in Periodic Media 2013, 58 (3):672 Journal of Scientific Computing
    Publisher
    Springer Nature
    Journal
    Journal of Scientific Computing
    DOI
    10.1007/s10915-013-9747-3
    arXiv
    1209.5164
    Additional Links
    http://link.springer.com/10.1007/s10915-013-9747-3
    http://arxiv.org/abs/1209.5164
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10915-013-9747-3
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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