Effective rankine-hugoniot conditions for shock waves in periodic media
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
Date
2020-07-28Preprint Posting Date
2019-09-11Online Publication Date
2020-07-28Print Publication Date
2020Embargo End Date
2021-01-13Submitted Date
2019-09-11Permanent link to this record
http://hdl.handle.net/10754/659990
Metadata
Show full item recordAbstract
Solutions of first-order nonlinear hyperbolic conservation laws typically develop shocks infinite time even from smooth initial conditions. However, in heterogeneous media with rapid spatial variation, shock formation may be delayed or avoided. When shocks do form in such media, their speed of propagation depends on the material structure. We investigate conditions for shock formation and propagation in heterogeneous media. We focus on the propagation of plane waves in two-dimensional media with a periodic structure that changes in only one direction. We propose an estimate for the speed of the shocks that is based on the Rankine-Hugoniot conditions applied to a leading-order homogenized (constant coefficient) system. We verify this estimate via numerical simulations using different nonlinear constitutive relations and layered and smoothly varying media with a periodic structure. In addition, we discuss conditions and regimes under which shocks form in this type of media.Citation
Ketcheson, D. I., & Quezada de Luna, M. (2020). Effective Rankine–Hugoniot conditions for shock waves in periodic media. Communications in Mathematical Sciences, 18(4), 1023–1040. doi:10.4310/cms.2020.v18.n4.a6Sponsors
This work was supported by funding from King Abdullah University of Science & Technology (KAUST).Publisher
International Press of BostonarXiv
1909.04937Additional Links
https://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0018/0004/a006/ae974a485f413a2113503eed53cd6c53
10.4310/CMS.2020.V18.N4.A6