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Duality based boundary treatment for the Euler and Navier-Stokes equations
Uppsala University, Department of Information Technology.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2013 (English)In: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, 1-19 p.Conference paper (Other academic)
Abstract [en]

In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions.

According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals.

Place, publisher, year, edition, pages
2013. 1-19 p.
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-96812DOI: 10.2514/6.2013-2959OAI: diva2:643644
21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, USA, 2013
Available from: 2013-08-28 Created: 2013-08-27 Last updated: 2014-12-03

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Nordström, Jan
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