Modeling of turbulent fluid flow based on the solution of the Mathieu equation
Objective. This work examines the problem of fluid flow simulation in a turbulent regime. The main reasons why turbulent flow occurs are due to the existence of high velocities of movement in fluids; besides that, there may be obstacles or changes in the shapes of flows. Method. To determine the cha...
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| Format: | Article |
| Language: | Russian |
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Dagestan State Technical University
2025-01-01
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| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
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| Online Access: | https://vestnik.dgtu.ru/jour/article/view/1617 |
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| _version_ | 1849250176753991680 |
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| author | V. V. Garbuzov A. P. Preobrazhensky |
| author_facet | V. V. Garbuzov A. P. Preobrazhensky |
| author_sort | V. V. Garbuzov |
| collection | DOAJ |
| description | Objective. This work examines the problem of fluid flow simulation in a turbulent regime. The main reasons why turbulent flow occurs are due to the existence of high velocities of movement in fluids; besides that, there may be obstacles or changes in the shapes of flows. Method. To determine the characteristics of a flow, it is proposed to use Mathieu’s equation. The main steps of the solution algorithm are presented for Mathieu functions that were used over the course of the computer program execution. Result. Upon evaluating eigenvalues, it is shown that it is necessary to rely on the corresponding transcendental equations. It is illustrated how modified Mathieu functions are calculated. It is indicated how calculations should be carried out in the case of a small parameter value in Mathieu functions. A block diagram of the executed turbulence modeling algorithm is presented. In order to conduct turbulence simulation, a GUI shell based on the Qt library was created in the Qt Creator environment. During the simulation process, the value of the Smagorinsky constant was chosen to be equal to 0.01. For the time step, a length value of 0.05 was selected. During the execution of the simulation, 2000 time steps were used. The simulation results were recorded every 10 steps. The results of the simulation are presented visually. Conclusion. A mathematical model has been created, on the basis of which there are possibilities for modeling turbulent media. The mathematical model has been constructed for various parameters during the flow of solid bodies by turbulent flows. |
| format | Article |
| id | doaj-art-9ae8cd758a004aef872ee8daf80ad8c8 |
| institution | Kabale University |
| issn | 2073-6185 2542-095X |
| language | Russian |
| publishDate | 2025-01-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj-art-9ae8cd758a004aef872ee8daf80ad8c82025-08-20T03:57:21ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2025-01-01514505910.21822/2073-6185-2024-51-4-50-59930Modeling of turbulent fluid flow based on the solution of the Mathieu equationV. V. Garbuzov0A. P. Preobrazhensky1Voronezh Institute of High TechnologiesVoronezh Institute of High TechnologiesObjective. This work examines the problem of fluid flow simulation in a turbulent regime. The main reasons why turbulent flow occurs are due to the existence of high velocities of movement in fluids; besides that, there may be obstacles or changes in the shapes of flows. Method. To determine the characteristics of a flow, it is proposed to use Mathieu’s equation. The main steps of the solution algorithm are presented for Mathieu functions that were used over the course of the computer program execution. Result. Upon evaluating eigenvalues, it is shown that it is necessary to rely on the corresponding transcendental equations. It is illustrated how modified Mathieu functions are calculated. It is indicated how calculations should be carried out in the case of a small parameter value in Mathieu functions. A block diagram of the executed turbulence modeling algorithm is presented. In order to conduct turbulence simulation, a GUI shell based on the Qt library was created in the Qt Creator environment. During the simulation process, the value of the Smagorinsky constant was chosen to be equal to 0.01. For the time step, a length value of 0.05 was selected. During the execution of the simulation, 2000 time steps were used. The simulation results were recorded every 10 steps. The results of the simulation are presented visually. Conclusion. A mathematical model has been created, on the basis of which there are possibilities for modeling turbulent media. The mathematical model has been constructed for various parameters during the flow of solid bodies by turbulent flows.https://vestnik.dgtu.ru/jour/article/view/1617simulationmathieu’s equationeigenfunctionfluid flowturbulencealgorithm |
| spellingShingle | V. V. Garbuzov A. P. Preobrazhensky Modeling of turbulent fluid flow based on the solution of the Mathieu equation Вестник Дагестанского государственного технического университета: Технические науки simulation mathieu’s equation eigenfunction fluid flow turbulence algorithm |
| title | Modeling of turbulent fluid flow based on the solution of the Mathieu equation |
| title_full | Modeling of turbulent fluid flow based on the solution of the Mathieu equation |
| title_fullStr | Modeling of turbulent fluid flow based on the solution of the Mathieu equation |
| title_full_unstemmed | Modeling of turbulent fluid flow based on the solution of the Mathieu equation |
| title_short | Modeling of turbulent fluid flow based on the solution of the Mathieu equation |
| title_sort | modeling of turbulent fluid flow based on the solution of the mathieu equation |
| topic | simulation mathieu’s equation eigenfunction fluid flow turbulence algorithm |
| url | https://vestnik.dgtu.ru/jour/article/view/1617 |
| work_keys_str_mv | AT vvgarbuzov modelingofturbulentfluidflowbasedonthesolutionofthemathieuequation AT appreobrazhensky modelingofturbulentfluidflowbasedonthesolutionofthemathieuequation |