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Computing hydrodynamic eigenmodes of channel flow with slip — A highly accurate algorithm

Raju, Suraj ; Gründing, Dirk ; Marić, Tomislav ; Bothe, Dieter ; Fricke, Mathis (2022)
Computing hydrodynamic eigenmodes of channel flow with slip — A highly accurate algorithm.
In: The Canadian Journal of Chemical Engineering, 2022, 100 (12)
doi: 10.26083/tuprints-00022891
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Computing hydrodynamic eigenmodes of channel flow with slip — A highly accurate algorithm
Language: English
Date: 23 December 2022
Place of Publication: Darmstadt
Year of primary publication: 2022
Publisher: John Wiley & Sons
Journal or Publication Title: The Canadian Journal of Chemical Engineering
Volume of the journal: 100
Issue Number: 12
DOI: 10.26083/tuprints-00022891
Corresponding Links:
Origin: Secondary publication DeepGreen

The transient start‐up flow solution with slip is a useful tool to verify computational fluid dynamics (CFD) simulations. However, a highly accurate, open‐source black box solution does not seem to be available. Our method provides a fast, automated, and rigorously verified open‐source implementation that can compute the hydrodynamic eigenmodes of a two‐dimensional channel flow beyond the standard floating‐point precision. This allows for a very accurate computation of the corresponding Fourier series solution. We prove that all roots are found in all special cases for the general flow problem with different slip lengths on the channel walls. The numerical results confirm analytically derived asymptotic power laws for the leading hydrodynamic eigenmode and the characteristic timescale in the limiting cases of small and large slip. The code repository including test cases is publicly available (DOI: 10.5281/zenodo.6806351). The Navier slip boundary condition for numerical simulations in OpenFOAM is also publicly available (DOI: 10.5281/zenodo.7037712).

Uncontrolled Keywords: boundary slip, computational fluid dynamics, hydrodynamic eigenmodes, instationary channel flow
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-228919
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Mathematical Modelling and Analysis
Date Deposited: 23 Dec 2022 13:49
Last Modified: 14 Nov 2023 19:05
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/22891
PPN: 503272833
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