Stokes flows in a two-dimensional bifurcation
The flow network model is an established approach to approximate pressure–flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille’s law, and thus neglect the impact of bifurcation geometry and...
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The Royal Society
2025-01-01
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| Series: | Royal Society Open Science |
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| Online Access: | https://royalsocietypublishing.org/doi/10.1098/rsos.241392 |
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| author | Yidan Xue Stephen J. Payne Sarah L. Waters |
| author_facet | Yidan Xue Stephen J. Payne Sarah L. Waters |
| author_sort | Yidan Xue |
| collection | DOAJ |
| description | The flow network model is an established approach to approximate pressure–flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille’s law, and thus neglect the impact of bifurcation geometry and finite-sized objects on the flow. We determine the impact of bifurcation geometry and objects by computing Stokes flows in a two-dimensional (2D) bifurcation using the Lightning-AAA Rational Stokes algorithm, a novel mesh-free algorithm for solving 2D Stokes flow problems utilizing an applied complex analysis approach based on rational approximation of the Goursat functions. We compute the flow conductances of bifurcations with different channel widths, bifurcation angles, curved boundary geometries and fixed circular objects. We quantify the difference between the computed conductances and their Poiseuille law approximations to demonstrate the importance of incorporating detailed bifurcation geometry into existing flow network models. We parametrize the flow conductances of 2D bifurcation as functions of the dimensionless parameters of bifurcation geometry and a fixed object using a machine learning approach, which is simple to use and provides more accurate approximations than Poiseuille’s law. Finally, the details of the 2D Stokes flows in bifurcations are presented. |
| format | Article |
| id | doaj-art-8b2e59740768410f961bda4a83cb5f64 |
| institution | Kabale University |
| issn | 2054-5703 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj-art-8b2e59740768410f961bda4a83cb5f642025-01-22T00:16:49ZengThe Royal SocietyRoyal Society Open Science2054-57032025-01-0112110.1098/rsos.241392Stokes flows in a two-dimensional bifurcationYidan Xue0Stephen J. Payne1Sarah L. Waters2Mathematical Institute, University of Oxford, Oxford, UKInstitute of Applied Mechanics, National Taiwan University, Taipei, TaiwanMathematical Institute, University of Oxford, Oxford, UKThe flow network model is an established approach to approximate pressure–flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille’s law, and thus neglect the impact of bifurcation geometry and finite-sized objects on the flow. We determine the impact of bifurcation geometry and objects by computing Stokes flows in a two-dimensional (2D) bifurcation using the Lightning-AAA Rational Stokes algorithm, a novel mesh-free algorithm for solving 2D Stokes flow problems utilizing an applied complex analysis approach based on rational approximation of the Goursat functions. We compute the flow conductances of bifurcations with different channel widths, bifurcation angles, curved boundary geometries and fixed circular objects. We quantify the difference between the computed conductances and their Poiseuille law approximations to demonstrate the importance of incorporating detailed bifurcation geometry into existing flow network models. We parametrize the flow conductances of 2D bifurcation as functions of the dimensionless parameters of bifurcation geometry and a fixed object using a machine learning approach, which is simple to use and provides more accurate approximations than Poiseuille’s law. Finally, the details of the 2D Stokes flows in bifurcations are presented.https://royalsocietypublishing.org/doi/10.1098/rsos.241392Stokes flowflow networkbifurcationlightning solverbiharmonic equation |
| spellingShingle | Yidan Xue Stephen J. Payne Sarah L. Waters Stokes flows in a two-dimensional bifurcation Royal Society Open Science Stokes flow flow network bifurcation lightning solver biharmonic equation |
| title | Stokes flows in a two-dimensional bifurcation |
| title_full | Stokes flows in a two-dimensional bifurcation |
| title_fullStr | Stokes flows in a two-dimensional bifurcation |
| title_full_unstemmed | Stokes flows in a two-dimensional bifurcation |
| title_short | Stokes flows in a two-dimensional bifurcation |
| title_sort | stokes flows in a two dimensional bifurcation |
| topic | Stokes flow flow network bifurcation lightning solver biharmonic equation |
| url | https://royalsocietypublishing.org/doi/10.1098/rsos.241392 |
| work_keys_str_mv | AT yidanxue stokesflowsinatwodimensionalbifurcation AT stephenjpayne stokesflowsinatwodimensionalbifurcation AT sarahlwaters stokesflowsinatwodimensionalbifurcation |