Computing hydrodynamic eigenmodes of channel flow with slip—A highly accurate algorithm. (3rd October 2022)

• Record Type: Journal Article
• Authors: Raju, Suraj; Gründing, Dirk; Marić, Tomislav; Bothe, Dieter; Fricke, Mathis
• Is Part Of: Canadian journal of chemical engineering. Volume 100:Number 12(2022)
• Page Start: 3531
• Page End: 3547
• Publication Date: 2022-10-03
• Subjects: boundary slip -- computational fluid dynamics -- hydrodynamic eigenmodes -- instationary channel flow; Chemical engineering -- Periodicals; Technology -- Periodicals; 660.05
• DOI: 10.1002/cjce.24598
• Languages: English
• ISSNs: 0008-4034

Abstract

Abstract: 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 ).