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A dual consistent summation-by-parts formulation for the linearized incompressible Navier-Stokes equations posed on deforming domains
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)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 376, p. 26p. 322-338Article in journal (Refereed) Published
Abstract [en]

In this article, well-posedness and dual consistency of the linearized constant coefficient incompressible Navier–Stokes equations posed on time-dependent spatial domains are studied. To simplify the derivation of the dual problem and improve the accuracy of gradients, the second order formulation is transformed to first order form. Boundary conditions that simultaneously lead to boundedness of the primal and dual problems are derived.Fully discrete finite difference schemes on summation-by-parts form, in combination with the simultaneous approximation technique, are constructed. We prove energy stability and discrete dual consistency and show how to construct the penalty operators such that the scheme automatically adjusts to the variations of the spatial domain. As a result of the aforementioned formulations, stability and discrete dual consistency follow simultaneously.The method is illustrated by considering a deforming time-dependent spatial domain in two dimensions. The numerical calculations are performed using high order operators in space and time. The results corroborate the stability of the scheme and the accuracy of the solution. We also show that linear functionals are superconverging. Additionally, we investigate the convergence of non-linear functionals and the divergence of the solution.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 376, p. 26p. 322-338
Keywords [en]
Incompressible Navier-Stokes equations, Deforming domain, Stability, Dual consistency, High order accuracy, Superconvergence
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-152031DOI: 10.1016/j.jcp.2018.09.006ISI: 000450337400016Scopus ID: 2-s2.0-85054431823OAI: oai:DiVA.org:liu-152031DiVA, id: diva2:1256446
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-12-13Bibliographically approved

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The full text will be freely available from 2020-10-06 09:11
Available from 2020-10-06 09:11

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Nikkar, SamiraNordström, Jan

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