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The spatial operator in the incompressible Navier-€“Stokes, Oseen and Stokes equations
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
2020 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 363, p. 1-21, article id 112857Article in journal (Refereed) Published
Abstract [en]

We investigate the spatial operator in the incompressible Navier–Stokes, Oseen and Stokes equations and show how to avoid singularities associated with null spaces by choosing specific boundary conditions. The theoretical results are derived for a general form of energy stable boundary conditions, and applied to a few commonly used ones.

The analysis is done on a system that simultaneously covers the nonlinear incompressible Navier–Stokes, the Oseen and the Stokes equations. When the spectrum of the spatial operator is investigated, we restrict the analysis to the Oseen and Stokes equations. The continuous analysis carries over to the discrete setting by using the summation-by-parts framework.

Place, publisher, year, edition, pages
Elsevier, 2020. Vol. 363, p. 1-21, article id 112857
Keywords [en]
Incompressible Navier-Stokes equations, Oseen equations, Stokes equations, Singularities, Semi-bounded operators, Eigenvalue problem
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-163769DOI: 10.1016/j.cma.2020.112857OAI: oai:DiVA.org:liu-163769DiVA, id: diva2:1394646
Available from: 2020-02-19 Created: 2020-02-19 Last updated: 2020-02-19Bibliographically approved

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The full text will be freely available from 2022-02-13 08:00
Available from 2022-02-13 08:00

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Nordström, JanLaurén, Fredrik

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  • apa
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  • de-DE
  • en-GB
  • en-US
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  • nn-NB
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  • Other locale
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Output format
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  • text
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