Central-Upwind Schemes for Two-Layer Shallow Water Equations

Handle URI:
http://hdl.handle.net/10754/597746
Title:
Central-Upwind Schemes for Two-Layer Shallow Water Equations
Authors:
Kurganov, Alexander; Petrova, Guergana
Abstract:
We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.
Citation:
Kurganov A, Petrova G (2009) Central-Upwind Schemes for Two-Layer Shallow Water Equations. SIAM Journal on Scientific Computing 31: 1742–1773. Available: http://dx.doi.org/10.1137/080719091.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2009
DOI:
10.1137/080719091
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
The work of this author was supported in part by NSF grant DMS-0610430. Department of Mathematics, Texas A & M University, College Station, TX 77843 ( gpetrova@math.tamu.edu). The work of this author was supported in part by NSF grants DMS-0505501 and DMS-0810869 and by award KUS-C1-016-04 made by King Abdullah University of Science and Technology ( KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorKurganov, Alexanderen
dc.contributor.authorPetrova, Guerganaen
dc.date.accessioned2016-02-25T12:55:58Zen
dc.date.available2016-02-25T12:55:58Zen
dc.date.issued2009-01en
dc.identifier.citationKurganov A, Petrova G (2009) Central-Upwind Schemes for Two-Layer Shallow Water Equations. SIAM Journal on Scientific Computing 31: 1742–1773. Available: http://dx.doi.org/10.1137/080719091.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/080719091en
dc.identifier.urihttp://hdl.handle.net/10754/597746en
dc.description.abstractWe derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThe work of this author was supported in part by NSF grant DMS-0610430. Department of Mathematics, Texas A & M University, College Station, TX 77843 ( gpetrova@math.tamu.edu). The work of this author was supported in part by NSF grants DMS-0505501 and DMS-0810869 and by award KUS-C1-016-04 made by King Abdullah University of Science and Technology ( KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectHyperbolic systems of conservation and balance lawsen
dc.subjectNonconservative productsen
dc.subjectSemidiscrete central-upwind schemesen
dc.subjectTwo-layer shallow water equationsen
dc.titleCentral-Upwind Schemes for Two-Layer Shallow Water Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionTulane University, New Orleans, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.