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Efficient Fully Discrete Summation-by-Parts Schemes for Unsteady Flow Problems: An Initial Investigation
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
2015 (English)In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 / [ed] Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Springer, 2015, 345-353 p.Chapter in book (Refereed)
Abstract [en]

We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for stiff unsteady flows with boundary layers. As a model problem for the Navier–Stokes equations we consider a two-dimensional advection-diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summation-by-parts form together with weak boundary conditions, leading to optimal stability estimates. For the time integration part we consider various forms of high order summation-by-parts operators, and compare the results to an existing popular fourth order diagonally implicit Runge-Kutta method. To solve the resulting fully discrete equation system, we employ a multi-grid scheme with dual time stepping.

Place, publisher, year, edition, pages
Springer, 2015. 345-353 p.
Series
Lecture Notes in Computational Science and Engineering, 106
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-123121DOI: 10.1007/978-3-319-19800-2_31ISI: 000368440400031ISBN: 978-3-319-19799-9 (print)ISBN: 978-3-319-19800-2 (print)OAI: oai:DiVA.org:liu-123121DiVA: diva2:876719
Available from: 2015-12-04 Created: 2015-12-04 Last updated: 2016-02-15Bibliographically approved

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