High-Order Wave Propagation Algorithms for Hyperbolic Systems

Handle URI:
http://hdl.handle.net/10754/333600
Title:
High-Order Wave Propagation Algorithms for Hyperbolic Systems
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X ) ; Parsani, Matteo ( 0000-0001-7300-1280 ) ; LeVeque, Randall J.
Abstract:
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Mathematics Group
Citation:
High-Order Wave Propagation Algorithms for Hyperbolic Systems 2013, 35 (1):A351 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Scientific Computing
Issue Date:
22-Jan-2013
DOI:
10.1137/110830320
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/110830320; http://arxiv.org/abs/1111.3499
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.authorParsani, Matteoen
dc.contributor.authorLeVeque, Randall J.en
dc.date.accessioned2014-11-03T16:18:15Z-
dc.date.available2014-11-03T16:18:15Z-
dc.date.issued2013-01-22en
dc.identifier.citationHigh-Order Wave Propagation Algorithms for Hyperbolic Systems 2013, 35 (1):A351 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/110830320en
dc.identifier.urihttp://hdl.handle.net/10754/333600en
dc.description.abstractWe present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/110830320en
dc.relation.urlhttp://arxiv.org/abs/1111.3499en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjecthyperbolic PDEsen
dc.subjecthigh-order methodsen
dc.subjectwave propagationen
dc.subjectGodunov-type methodsen
dc.subjectWENOen
dc.titleHigh-Order Wave Propagation Algorithms for Hyperbolic Systemsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Applied Mathematics, University of Washington, Seattle, WA 98195-2420en
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKetcheson, David I.en
kaust.authorParsani, Matteoen
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