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Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations
Uppsala University, Sweden.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, 135-153 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we derive new farfield boundary conditions for the time-dependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.

We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

Place, publisher, year, edition, pages
2014. Vol. 259, 135-153 p.
Keyword [en]
High order finite differences; Summation-by-parts; Superconvergence; Dual consistency; Stability
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-102292DOI: 10.1016/ 000329506500009OAI: diva2:675996
Available from: 2013-12-05 Created: 2013-12-05 Last updated: 2014-01-31Bibliographically approved

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