liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
Mathematisches Institut, Universität zu Köln, Köln, Germany.
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
Mathematisches Institut, Universität zu Köln, Köln, GermanyUniversity of Cologne.
Department of Mathematics, The Florida State University, Tallahassee, USA. (Department of Mathematics)
2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 340, p. 200-242Article in journal (Refereed) Published
Abstract [en]

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non- constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 340, p. 200-242
Keywords [en]
shallow water equations, discontinuous Galerkin spectral element method, summation- by-parts, entropy stability, well-balanced, discontinuous bathymetry
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156857DOI: 10.1016/j.jcp.2017.03.036ISI: 000401137900011Scopus ID: 2-s2.0-85016434943OAI: oai:DiVA.org:liu-156857DiVA, id: diva2:1315783
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-23Bibliographically approved

Open Access in DiVA

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry(4249 kB)0 downloads
File information
File name FULLTEXT01.pdfFile size 4249 kBChecksum SHA-512
e764c5181b49a09d88178f319c3582b62976fddd8653e183ec97cfeee53276eac6cf76e52555279e030821663d77112bc63924371932dc45981ad8945d87c5b2
Type fulltextMimetype application/pdf

Other links

Publisher's full textScopus

Authority records BETA

Winters, Andrew Ross

Search in DiVA

By author/editor
Winters, Andrew Ross
In the same journal
Journal of Computational Physics
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 2 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf