Stokes flows in a 2D bifurcation

Xue, Yidan ORCID: https://orcid.org/0000-0001-9532-8671, Payne, Stephen J. and Waters, Sarah L. 2023. Stokes flows in a 2D bifurcation. [Online]. arXiv: arXiv. Available at: https://arxiv.org/abs/2309.11230

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Abstract

The flow network model is an established approach to approximate pressure-flow relationships in a network, which has been widely used in many contexts. However, little is known about the impact of bifurcation geometry on such approximations, so the existing models mostly rely on unidirectional flow assumption and Poiseuille's law, and thus neglect the flow details at each bifurcation. In this work, we address these limitations by computing Stokes flows in a 2D bifurcation using LARS (Lightning-AAA Rational Stokes), a novel mesh-free algorithm for solving 2D Stokes flow problems utilising an applied complex analysis approach based on rational approximation of the Goursat functions. Using our 2D bifurcation model, we show that the fluxes in two child branches depend on not only pressures and widths of inlet and outlet branches, as most previous studies have assumed, but also detailed bifurcation geometries (e.g. bifurcation angle), which were not considered in previous studies. The 2D Stokes flow simulations allow us to represent the relationship between pressures and fluxes of a bifurcation using an updated flow network, which considers the bifurcation geometry and can be easily incorporated into previous flow network approaches. The errors in the flow conductance of a channel in a bifurcation approximated using Poiseuille's law can be greater than 16%, when the centreline length is twice the inlet channel width and the bifurcation geometry is highly asymmetric. In addition, we present details of 2D Stokes flow features, such as flow separation in a bifurcation and flows around fixed objects at different locations, which previous flow network models cannot capture. These findings suggest the importance of incorporating detailed flow modelling techniques alongside existing flow network approaches when solving complex flow problems.

Item Type:	Website Content
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	arXiv
Last Modified:	08 Jan 2024 13:45
URI:	https://orca.cardiff.ac.uk/id/eprint/165288

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