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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Autores principales:	Ali Ercan, M. Levent Kavvas
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/a5d69007b2b24e6790fc09266b51f514
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spelling	oai:doaj.org-article:a5d69007b2b24e6790fc09266b51f5142021-12-02T15:05:55ZScaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations10.1038/s41598-017-06669-z2045-2322https://doaj.org/article/a5d69007b2b24e6790fc09266b51f5142017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-06669-zhttps://doaj.org/toc/2045-2322Abstract 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.Ali ErcanM. Levent KavvasNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Ali Ercan M. Levent Kavvas Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations
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.
format	article
author	Ali Ercan M. Levent Kavvas
author_facet	Ali Ercan M. Levent Kavvas
author_sort	Ali Ercan
title	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_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_sort	scaling relations and self-similarity of 3-dimensional reynolds-averaged navier-stokes equations
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/a5d69007b2b24e6790fc09266b51f514
work_keys_str_mv	AT aliercan scalingrelationsandselfsimilarityof3dimensionalreynoldsaveragednavierstokesequations AT mleventkavvas scalingrelationsandselfsimilarityof3dimensionalreynoldsaveragednavierstokesequations
_version_	1718388663156473856

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations

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