Shock dynamics in layered periodic media

Handle URI:
http://hdl.handle.net/10754/333598
Title:
Shock dynamics in layered periodic media
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Leveque, Randall J.
Abstract:
Solutions of constant-coeffcient nonlinear hyperbolic PDEs generically develop shocks, even if the initial data is smooth. Solutions of hyperbolic PDEs with variable coeffcients can behave very differently. We investigate formation and stability of shock waves in a one-dimensional periodic layered medium by a computational study of time-reversibility and entropy evolution. We find that periodic layered media tend to inhibit shock formation. For small initial conditions and large impedance variation, no shock formation is detected even after times much greater than the time of shock formation in a homogeneous medium. Furthermore, weak shocks are observed to be dynamically unstable in the sense that they do not lead to significant long-term entropy decay. We propose a characteristic condition for admissibility of shocks in heterogeneous media that generalizes the classical Lax entropy condition and accurately predicts the formation or absence of shocks in these media.
KAUST Department:
Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Shock dynamics in layered periodic media 2012, 10 (3):859 Communications in Mathematical Sciences
Publisher:
International Press
Journal:
Communications in Mathematical Sciences
Issue Date:
2012
DOI:
10.4310/CMS.2012.v10.n3.a7
ARXIV:
arXiv:1105.2892
Type:
Article
ISSN:
15396746; 19450796
Additional Links:
http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0010/0003/a007/; http://arxiv.org/abs/1105.2892
Appears in Collections:
Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorLeveque, Randall J.en
dc.date.accessioned2014-11-03T16:17:16Z-
dc.date.available2014-11-03T16:17:16Z-
dc.date.issued2012en
dc.identifier.citationShock dynamics in layered periodic media 2012, 10 (3):859 Communications in Mathematical Sciencesen
dc.identifier.issn15396746en
dc.identifier.issn19450796en
dc.identifier.doi10.4310/CMS.2012.v10.n3.a7en
dc.identifier.urihttp://hdl.handle.net/10754/333598en
dc.description.abstractSolutions of constant-coeffcient nonlinear hyperbolic PDEs generically develop shocks, even if the initial data is smooth. Solutions of hyperbolic PDEs with variable coeffcients can behave very differently. We investigate formation and stability of shock waves in a one-dimensional periodic layered medium by a computational study of time-reversibility and entropy evolution. We find that periodic layered media tend to inhibit shock formation. For small initial conditions and large impedance variation, no shock formation is detected even after times much greater than the time of shock formation in a homogeneous medium. Furthermore, weak shocks are observed to be dynamically unstable in the sense that they do not lead to significant long-term entropy decay. We propose a characteristic condition for admissibility of shocks in heterogeneous media that generalizes the classical Lax entropy condition and accurately predicts the formation or absence of shocks in these media.en
dc.language.isoenen
dc.publisherInternational Pressen
dc.relation.urlhttp://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0010/0003/a007/en
dc.relation.urlhttp://arxiv.org/abs/1105.2892en
dc.rightsArchived with thanks to Communications in Mathematical Sciencesen
dc.subjectshock wavesen
dc.subjectperiodic mediaen
dc.subjectdispersive shocksen
dc.subjectsolitary wavesen
dc.titleShock dynamics in layered periodic mediaen
dc.typeArticleen
dc.contributor.departmentNumerical Mathematics Groupen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCommunications in Mathematical Sciencesen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195-2420, USAen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1105.2892en
kaust.authorKetcheson, David I.en
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