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An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations
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)Report (Other academic)
Abstract [en]

The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.

The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.

We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. , p. 42
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2019:7
Keywords [en]
Compressible fluid, incompressible fluid, Navier-Stokes equations, energy estimate, interface conditions, stability
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-158905ISRN: LiTH-MAT-R--2019/07--SEOAI: oai:DiVA.org:liu-158905DiVA, id: diva2:1337838
Available from: 2019-07-17 Created: 2019-07-17 Last updated: 2019-07-29Bibliographically approved

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Ghasemi Zinatabadi, FatemehNordström, Jan
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CiteExportLink to record
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Citation style
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