Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities
A two-dimensional periodic Stokes flow of viscous incompressible fluid in a rectangular cavity with constant velocities applied to the top and bottom walls is considered. The study of advection regimes is reduced to the sequential solving of two problems. To solve the first problem, the analytical m...
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MDPI AG
2024-12-01
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| author | Valentyn Sobchuk Oleksandr Kurylko Oleksandr Boryseiko Oleh Perehuda Iryna Lebedyeva Igor Ulitko Olena Vashchilina |
| author_facet | Valentyn Sobchuk Oleksandr Kurylko Oleksandr Boryseiko Oleh Perehuda Iryna Lebedyeva Igor Ulitko Olena Vashchilina |
| author_sort | Valentyn Sobchuk |
| collection | DOAJ |
| description | A two-dimensional periodic Stokes flow of viscous incompressible fluid in a rectangular cavity with constant velocities applied to the top and bottom walls is considered. The study of advection regimes is reduced to the sequential solving of two problems. To solve the first problem, the analytical method of superposition, which allows one to obtain any desired accuracy of the velocity field, is used. To solve the second problem, which is associated with obtaining the trajectories of individual fluid particles, numerical calculations of the Cauchy problem were performed. An analysis of the boundary conditions accuracy was performed based on the control of local integration. The advection of the selected volume of fluid in the rectangular cavity under the periodic motion of walls for a finite period time based on piecewise spline cubic interpolation is modeled. The obtained numerical results agree with well-known experimental data. |
| format | Article |
| id | doaj-art-3357b95654504392b9aed14d67bb6cab |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-3357b95654504392b9aed14d67bb6cab2025-01-24T13:22:07ZengMDPI AGAxioms2075-16802024-12-01141310.3390/axioms14010003Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant VelocitiesValentyn Sobchuk0Oleksandr Kurylko1Oleksandr Boryseiko2Oleh Perehuda3Iryna Lebedyeva4Igor Ulitko5Olena Vashchilina6Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, UkraineFaculty of Information Technology, Taras Shevchenko National University of Kyiv, 24 Bohdana Havrylyshyna Street, 04116 Kyiv, UkraineA two-dimensional periodic Stokes flow of viscous incompressible fluid in a rectangular cavity with constant velocities applied to the top and bottom walls is considered. The study of advection regimes is reduced to the sequential solving of two problems. To solve the first problem, the analytical method of superposition, which allows one to obtain any desired accuracy of the velocity field, is used. To solve the second problem, which is associated with obtaining the trajectories of individual fluid particles, numerical calculations of the Cauchy problem were performed. An analysis of the boundary conditions accuracy was performed based on the control of local integration. The advection of the selected volume of fluid in the rectangular cavity under the periodic motion of walls for a finite period time based on piecewise spline cubic interpolation is modeled. The obtained numerical results agree with well-known experimental data.https://www.mdpi.com/2075-1680/14/1/3Stokes flowadvectionmixingrectangular cavitysimulation |
| spellingShingle | Valentyn Sobchuk Oleksandr Kurylko Oleksandr Boryseiko Oleh Perehuda Iryna Lebedyeva Igor Ulitko Olena Vashchilina Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities Axioms Stokes flow advection mixing rectangular cavity simulation |
| title | Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities |
| title_full | Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities |
| title_fullStr | Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities |
| title_full_unstemmed | Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities |
| title_short | Simulation of the Advection Process of Stokes Flow Inside a Rectangular Cavity Under Constant Velocities |
| title_sort | simulation of the advection process of stokes flow inside a rectangular cavity under constant velocities |
| topic | Stokes flow advection mixing rectangular cavity simulation |
| url | https://www.mdpi.com/2075-1680/14/1/3 |
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