Steiner, J, Ruprecht, D orcid.org/0000-0003-1904-2473, Speck, R et al. (1 more author) (2015) Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number. In: Abdulle, A, Deparis, S, Kressner, D, Nobile, F and Picasso, M, (eds.) Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications. Numerical Mathematics and Advanced Applications - ENUMATH 2013, 26-30 Aug 2013, Lausanne, Switzerland. Lecture Notes in Computational Science and Engineering, 103 . Springer Verlag (Germany) , pp. 195-202. ISBN 978-3-319-10704-2
Abstract
The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.
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Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | (c) Springer International Publishing Switzerland 2015. This is an author produced version of a paper published in Lecture Notes in Computational Science and Engineering. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-10705-9_19 |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Nov 2015 15:31 |
Last Modified: | 16 Jan 2018 15:59 |
Published Version: | http://dx.doi.org/10.1007/978-3-319-10705-9_19 |
Status: | Published |
Publisher: | Springer Verlag (Germany) |
Series Name: | Lecture Notes in Computational Science and Engineering |
Identification Number: | 10.1007/978-3-319-10705-9_19 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90736 |