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Stable Robin solid wall boundary conditions for the Navier-Stokes equations
Uppsala University, Department of Information Technology.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0002-7972-6183
2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 19, 7519-7532 p.Article in journal (Refereed) Published
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 first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.

The discretization is done using finite differences 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 flows ranging from no-slip to almost full slip.

Place, publisher, year, edition, pages
2011. Vol. 230, no 19, 7519-7532 p.
Keyword [en]
Navier–Stokes; Robin boundary conditions; Well-posedness; Stability; High order accuracy; Summation-By-Parts
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-70019DOI: 10.1016/ 000294979400027OAI: diva2:435413
Original Publication: Jens Berg and Jan Nordström, Stable Robin solid wall boundary conditions for the Navier-Stokes equations, 2011, Journal of Computational Physics, (230), 19, 7519-7532. Copyright: Elsevier Available from: 2011-08-23 Created: 2011-08-15 Last updated: 2013-08-30Bibliographically approved

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