Numerical study of transitions in lid-driven flows in shallow cavities
In this article, three dimensional (3D) lid-driven flow in shallow cavities with a unit square base are studied. The numerical solution of the Navier–Stokes equations modeling incompressible viscous fluid flow in a cavity is obtained via a methodology combining a first order accurate operator-splitt...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.166/ |
| _version_ | 1797651385896927232 |
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| author | Pan, Tsorng-Whay Chiu, Shang-Huan Guo, Aixia He, Jiwen |
| author_facet | Pan, Tsorng-Whay Chiu, Shang-Huan Guo, Aixia He, Jiwen |
| author_sort | Pan, Tsorng-Whay |
| collection | DOAJ |
| description | In this article, three dimensional (3D) lid-driven flow in shallow cavities with a unit square base are studied. The numerical solution of the Navier–Stokes equations modeling incompressible viscous fluid flow in a cavity is obtained via a methodology combining a first order accurate operator-splitting scheme, a $L^2$-projection Stokes solver, a wave-like equation treatment of the advection and finite element space approximations. Numerical results of a lid-driven flow in a cubic cavity show a good agreement with those reported in literature. The critical Reynolds numbers ($\mathit{Re}_{\mathrm{cr}}$) for having flow with increasing of oscillating amplitude (a Hopf bifurcation) in different shallow cavities are obtained and associated oscillating modes are studied. |
| first_indexed | 2024-03-11T16:15:11Z |
| format | Article |
| id | doaj.art-70f1c8700d56450783124f4b3ee8925e |
| institution | Directory Open Access Journal |
| issn | 1873-7234 |
| language | English |
| last_indexed | 2024-03-11T16:15:11Z |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj.art-70f1c8700d56450783124f4b3ee8925e2023-10-24T14:21:34ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-02-0111710.5802/crmeca.16610.5802/crmeca.166Numerical study of transitions in lid-driven flows in shallow cavitiesPan, Tsorng-Whay0https://orcid.org/0000-0002-1526-2615Chiu, Shang-Huan1https://orcid.org/0000-0003-0534-4286Guo, Aixia2https://orcid.org/0000-0003-0542-0920He, Jiwen3Department of Mathematics, University of Houston, Houston, Texas 77204, USADepartment of Mathematics, Lehigh University, Bethlehem, PA, 18015, USADepartment of Mathematics, University of Houston, Houston, Texas 77204, USADepartment of Mathematics, University of Houston, Houston, Texas 77204, USAIn this article, three dimensional (3D) lid-driven flow in shallow cavities with a unit square base are studied. The numerical solution of the Navier–Stokes equations modeling incompressible viscous fluid flow in a cavity is obtained via a methodology combining a first order accurate operator-splitting scheme, a $L^2$-projection Stokes solver, a wave-like equation treatment of the advection and finite element space approximations. Numerical results of a lid-driven flow in a cubic cavity show a good agreement with those reported in literature. The critical Reynolds numbers ($\mathit{Re}_{\mathrm{cr}}$) for having flow with increasing of oscillating amplitude (a Hopf bifurcation) in different shallow cavities are obtained and associated oscillating modes are studied.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.166/Lid driven cavity flowShallow cavityTaylor–Görtler-like vorticesHopf bifurcationProjection method |
| spellingShingle | Pan, Tsorng-Whay Chiu, Shang-Huan Guo, Aixia He, Jiwen Numerical study of transitions in lid-driven flows in shallow cavities Comptes Rendus. Mécanique Lid driven cavity flow Shallow cavity Taylor–Görtler-like vortices Hopf bifurcation Projection method |
| title | Numerical study of transitions in lid-driven flows in shallow cavities |
| title_full | Numerical study of transitions in lid-driven flows in shallow cavities |
| title_fullStr | Numerical study of transitions in lid-driven flows in shallow cavities |
| title_full_unstemmed | Numerical study of transitions in lid-driven flows in shallow cavities |
| title_short | Numerical study of transitions in lid-driven flows in shallow cavities |
| title_sort | numerical study of transitions in lid driven flows in shallow cavities |
| topic | Lid driven cavity flow Shallow cavity Taylor–Görtler-like vortices Hopf bifurcation Projection method |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.166/ |
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