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
Encapsulated high order difference operators on curvilinear non-conforming grids
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 385, p. 209-224Article in journal (Refereed) Published
Abstract [en]

Constructing stable difference schemes on complex geometries is an arduous task. Even fairly simple partial differential equations end up very convoluted in their discretized form, making them difficult to implement and manage. Spatial discretizations using so called summation-by-parts operators have mitigated this issue to some extent, particularly on rectangular domains, making it possible to formulate stable discretizations in a compact and understandable manner. However, the simplicity of these formulations is lost for curvilinear grids, where the standard procedure is to transform the grid to a rectangular one, and change the structure of the original equation. In this paper we reinterpret the grid transformation as a transformation of the summation-by-parts operators. This results in operators acting directly on the curvilinear grid. Together with previous developments in the field of nonconforming grid couplings we can formulate simple, implementable, and provably stable schemes on general nonconforming curvilinear grids. The theory is applicable to methods on summation-by-parts form, including finite differences, discontinuous Galerkin spectral element, finite volume, and flux reconstruction methods. Time dependent advection–diffusion simulations corroborate the theoretical development.

Place, publisher, year, edition, pages
2019. Vol. 385, p. 209-224
Keywords [en]
Non-conforming grids, Curvilinear mappings, Weak interface couplings, Summation-by-parts, Stability, Energy method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-154938DOI: 10.1016/j.jcp.2019.02.007ISI: 000460889200011OAI: oai:DiVA.org:liu-154938DiVA, id: diva2:1294075
Available from: 2019-03-06 Created: 2019-03-06 Last updated: 2019-04-01

Open Access in DiVA

The full text will be freely available from 2021-02-26 12:23
Available from 2021-02-26 12:23

Other links

Publisher's full text

Authority records BETA

Ålund, OskarNordström, Jan

Search in DiVA

By author/editor
Ålund, OskarNordström, Jan
By organisation
Computational MathematicsFaculty of Science & Engineering
In the same journal
Journal of Computational Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 51 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