Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations
Abstract Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the deriv...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2017-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-017-06669-z |
| _version_ | 1818343787624136704 |
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| author | Ali Ercan M. Levent Kavvas |
| author_facet | Ali Ercan M. Levent Kavvas |
| author_sort | Ali Ercan |
| collection | DOAJ |
| description | Abstract Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions. |
| first_indexed | 2024-12-13T16:36:08Z |
| format | Article |
| id | doaj.art-a5d69007b2b24e6790fc09266b51f514 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-13T16:36:08Z |
| publishDate | 2017-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-a5d69007b2b24e6790fc09266b51f5142022-12-21T23:38:24ZengNature PortfolioScientific Reports2045-23222017-07-017111010.1038/s41598-017-06669-zScaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes EquationsAli Ercan0M. Levent Kavvas1J. Amorocho Hydraulics Laboratory, Department of Civil and Environmental Engineering, University of CaliforniaHydrologic Research Laboratory and J. Amorocho Hydraulics Laboratory, Department of Civil and Environmental Engineering, University of CaliforniaAbstract Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.https://doi.org/10.1038/s41598-017-06669-z |
| spellingShingle | Ali Ercan M. Levent Kavvas Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations Scientific Reports |
| title | Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations |
| title_full | Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations |
| title_fullStr | Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations |
| title_full_unstemmed | Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations |
| title_short | Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations |
| title_sort | scaling relations and self similarity of 3 dimensional reynolds averaged navier stokes equations |
| url | https://doi.org/10.1038/s41598-017-06669-z |
| work_keys_str_mv | AT aliercan scalingrelationsandselfsimilarityof3dimensionalreynoldsaveragednavierstokesequations AT mleventkavvas scalingrelationsandselfsimilarityof3dimensionalreynoldsaveragednavierstokesequations |