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

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: https://doi.org/10.5281/zenodo.6806351). The Navier slip boundary condition for numerical simulations in OpenFOAM is also publicly available (DOI: https://doi.org/10.5281/zenodo.7037712).

Preface to the computational fluid dynamics for chemical and process engineering special issue section

“…While the previously mentioned studies are concerned with simulations at the apparatus‐scale, detailed numerical studies by Konstantinidis et al, [ 4 ] Raju et al, [ 5 ] Begemann et al, [ 6 ] and Vasquez Giuliano et al [ 7 ] focus on local phenomena and processes at the micro‐ to nano‐scale. Both Konstantinidis et al [ 4 ] and Raju et al [ 5 ] are motivated by wetting process simulations.…”

“…While the previously mentioned studies are concerned with simulations at the apparatus‐scale, detailed numerical studies by Konstantinidis et al, [ 4 ] Raju et al, [ 5 ] Begemann et al, [ 6 ] and Vasquez Giuliano et al [ 7 ] focus on local phenomena and processes at the micro‐ to nano‐scale. Both Konstantinidis et al [ 4 ] and Raju et al [ 5 ] are motivated by wetting process simulations. In Konstantinidis et al’s work, [ 4 ] the authors use a combined immersed‐boundary (IB) volume‐of‐fluid (VOF) method in combination with the Navier‐slip boundary condition to disclose coalescence and jumping of microdroplets on superhydrophobic surfaces.…”

“…The authors, in particular, ‘outline the difficulties and limitations encountered by all numerical frameworks when capturing the actual movement of the three‐phase contact line and the corresponding dynamics of the contact angle’. This is also discussed by Raju et al, [ 5 ] which provides a free and publicly available means for the verification of the Navier‐slip boundary condition using a transient start‐up flow solution with slip. In Begemann et al’s study, [ 6 ] the emulsification process in homogeneous isotropic turbulence is studied using a VOF method, disclosing the effects of turbulence intensity and surface tension.…”