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Stable Robin boundary conditions for the Navier-Stokes equations
Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2011 (English)Report (Other academic)
Abstract [en]

In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier-Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the rst order slip-ow boundary conditions. The formulation is uni-form and the transitions between dierent boundary conditions are done by a change of parameters. We give dierent sharp energy estimates depending on the choice of parameters.

The discretization is done using nite dierences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of ows ranging from no-slip to substantial slip.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 20 p.
Series
, Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011:012
Keyword [en]
Navier-Stokes, Robin boundary conditions, Well-posedness, Sta-bility, High order accuracy, Summation-By-Parts, Weak boundary conditions
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-67778OAI: oai:DiVA.org:liu-67778DiVA: diva2:412803
Available from: 2011-05-09 Created: 2011-04-26 Last updated: 2013-08-30Bibliographically approved

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Nordström, Jan
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Scientific ComputingThe Institute of Technology
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