onr:"swepub:oai:DiVA.org:liu-156857"
Search: onr:"swepub:oai:DiVA.org:liu-156857" > An entropy stable n...
- 1 of 1
- Previous record
- Next record
- To hitlist
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
-
- Wintermeyer, Niklas (author)
- Mathematisches Institut, Universität zu Köln, Köln, Germany
-
- Winters, Andrew Ross (author)
- Mathematisches Institut, Universität zu Köln, Köln, Germany
-
- Gassner, Gregor J (author)
- Mathematisches Institut, Universität zu Köln, Köln, GermanyUniversity of Cologne
- show more...
- show less...
- (creator_code:org_t)
- Elsevier, 2017
- 2017
- English.
- In: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 340, s. 200-242
- Journal article (peer-reviewed)
Abstract
Subject headings
Close
- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- shallow water equations
- discontinuous Galerkin spectral element method
- summation- by-parts
- entropy stability
- well-balanced
- discontinuous bathymetry
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
- Journal of Computational Physics (Search for host publication in LIBRIS)
To the university's database
- 1 of 1
- Previous record
- Next record
- To hitlist
Find more in SwePub
- By the author/editor
- Wintermeyer, Nik ...
- Winters, Andrew ...
- Gassner, Gregor ...
- Kopriva, David A
- About the subject
-
- NATURAL SCIENCES
- NATURAL SCIENCES
- and Mathematics
- and Computational Ma ...
- Articles in the publication
- Journal of Compu ...
- By the university
- Linköping University
Search outside SwePub
- Extend your search to:
- Google Book Search
- Google Scholar
Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.
- Copyright © LIBRIS - National Library Systems
- LIBRIS.kb.se
