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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. (Publisher's Version)
In: The Canadian Journal of Chemical Engineering, 100 (12), pp. 3531-3547. John Wiley & Sons, e-ISSN 1939-019X,
DOI: 10.26083/tuprints-00022891,

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Item Type: Article
Origin: Secondary publication DeepGreen
Status: Publisher's Version
Title: Computing hydrodynamic eigenmodes of channel flow with slip — A highly accurate algorithm
Language: English

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).

Journal or Publication Title: The Canadian Journal of Chemical Engineering
Volume of the journal: 100
Issue Number: 12
Place of Publication: Darmstadt
Publisher: John Wiley & Sons
Uncontrolled Keywords: boundary slip, computational fluid dynamics, hydrodynamic eigenmodes, instationary channel flow
Classification DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Divisions: 04 Department of Mathematics > Mathematical Modelling and Analysis
Date Deposited: 23 Dec 2022 13:49
Last Modified: 05 Jan 2023 07:17
DOI: 10.26083/tuprints-00022891
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-228919
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/22891
PPN: 503272833
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