Digitala Vetenskapliga Arkivet

Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
Mathematisches Institut, Universität zu Köln, Köln, Germany.
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
Department of Mathematics, The Florida State University, Tallahassee, US.
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 327, p. 39-66Article in journal (Refereed) Published
Abstract [en]

Fisher and Carpenter (High-order entropy stable finite difference schemes for non-linear conservation laws: Finite domains, Journal of Computational Physics, 252:518–557, 2013) found a remarkable equivalence of general diagonal norm high-order summation-by- parts operators to a subcell based high-order finite volume formulation. This equivalence enables the construction of provably entropy stable schemes by a specific choice of the sub-cell finite volume flux. We show that besides the construction of entropy stable high order schemes, a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms. Thus, by changing the subcell finite volume flux to a specific choice, we are able to generate, in a systematic way, all common split forms of the compressible Euler advection terms, such as the Ducros splitting and the Kennedy and Gruber splitting. Although these split forms are not entropy stable, we present a systematic way to prove which of those split forms are at least kinetic energy preserving. With this, we show we construct a unified high-order split form DG framework. We investigate with three dimensional numerical simulations of the inviscid Taylor-Green vortex and show that the new split forms enhance the robustness of high order simulations in comparison to the standard scheme when solving turbulent vortex dominated flows. In fact, we show that for certain test cases, the novel split form discontinuous Galerkin schemes are more robust than the discontinuous Galerkin scheme with over-integration.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 327, p. 39-66
Keywords [en]
Ducros splitting, Kennedy and Gruber splitting, kinetic energy, discontinuous Galerkin spectral element method, 3D compressible Euler equations, Taylor-Green vortex, split form
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156866DOI: 10.1016/j.jcp.2016.09.013ISI: 000386069200003Scopus ID: 2-s2.0-84988891066OAI: oai:DiVA.org:liu-156866DiVA, id: diva2:1315789
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-24Bibliographically approved

Open Access in DiVA

Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations(1362 kB)496 downloads
File information
File name FULLTEXT01.pdfFile size 1362 kBChecksum SHA-512
1bd65d88a7e937c3a02b8e5b1c0c8b4ef654053df09704b014b9da6d9e3f00247e7f02ae195cddfef46bff4725f041a77e766a9991fbbb3a33addd1987e9f8a0
Type fulltextMimetype application/pdf

Other links

Publisher's full textScopus

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
Total: 496 downloads
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: 182 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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