A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes
Autor(a) principal: | |
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Data de Publicação: | 2024 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | The Journal of Engineering and Exact Sciences |
Texto Completo: | https://periodicos.ufv.br/jcec/article/view/17579 |
Resumo: | This study delves into the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes, employing the Smagorinsky Model (SM). By treating the model as inherently discrete, we implement a semi-implicit time discretization using the Euler method. This approach includes comprehensive stability analyses, applicable to a spectrum of flow regimes, and an exploration of the asymptotic energy balance dynamics during fluid movements. The primary contribution of this study is found in its methodical approach to the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes using the Smagorinsky Model (SM). The adoption of a semi-implicit time discretization with the Euler method, coupled with a meticulous analysis of energy balance, establishes a robust foundation adaptable to diverse flow conditions. |
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A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimesUno Un análisis matemático para la solución débil aproximada del modelo de Smagorinsky para diferentes regímenes de flujoUn Une analyse mathématique pour la solution faible approchée du modèle de Smagorinsky pour différents régimes d'écoulementUma análise matemática para a solução fraca aproximada do Modelo Smagorinsky para diferentes regimes de fluxoSmagorinsky model.Weak Solution.Navier–Stokes equations.Asymptotic Balance.Modelo de Smagorinsky.Solução Fraca.Equações de Navier–Stokes.Balanço Assintótico.Modelo de Smagorinsky.Solución débil.Ecuaciones de Navier-Stokes.Modèle Smagorinsky.Solution faible.Équations de Navier-Stokes.This study delves into the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes, employing the Smagorinsky Model (SM). By treating the model as inherently discrete, we implement a semi-implicit time discretization using the Euler method. This approach includes comprehensive stability analyses, applicable to a spectrum of flow regimes, and an exploration of the asymptotic energy balance dynamics during fluid movements. The primary contribution of this study is found in its methodical approach to the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes using the Smagorinsky Model (SM). The adoption of a semi-implicit time discretization with the Euler method, coupled with a meticulous analysis of energy balance, establishes a robust foundation adaptable to diverse flow conditions.Este estudio investiga la aproximación numérica de ecuaciones de Navier-Stokes no estacionarias en regímenes turbulentos, empleando el modelo de Smagorinsky (SM). Al tratar el modelo como inherentemente discreto, implementamos una discretización temporal semiimplícita utilizando el método de Euler. Este enfoque incluye análisis integrales de estabilidad, aplicables a un espectro de regímenes de flujo, y una exploración de la dinámica asintótica del equilibrio energético durante los movimientos de los fluidos. La principal contribución de este estudio radica en su enfoque metódico a la aproximación numérica de ecuaciones de Navier-Stokes no estacionarias dentro de regímenes turbulentos utilizando el Modelo de Smagorinsky (SM). La adopción de una discretización temporal semi-implícita con el método de Euler, combinada con un análisis meticuloso del balance energético, establece una base robusta y adaptable a diferentes condiciones de flujo.Cette étude étudie l'approximation numérique des équations de Navier-Stokes non stationnaires dans des régimes turbulents, en utilisant le modèle Smagorinsky (SM). En traitant le modèle comme intrinsèquement discret, nous implémentons une discrétisation temporelle semi-implicite en utilisant la méthode d'Euler. Cette approche comprend des analyses complètes de stabilité, applicables à un spectre de régimes d'écoulement, et une exploration de la dynamique asymptotique du bilan énergétique lors des mouvements de fluides. La principale contribution de cette étude réside dans son approche méthodique de l'approximation numérique des équations de Navier-Stokes non stationnaires dans des régimes turbulents à l'aide du modèle de Smagorinsky (SM). L'adoption d'une discrétisation temporelle semi-implicite avec la méthode d'Euler, combinée à une analyse minutieuse du bilan énergétique, établit une base robuste et adaptable à différentes conditions d'écoulement.Este estudo investiga a aproximação numérica de equações não estacionárias de Navier-Stokes em regimes turbulentos, empregando o Modelo Smagorinsky (SM). Ao tratar o modelo como inerentemente discreto, implementamos uma discretização temporal semi-implícita usando o método de Euler. Esta abordagem inclui análises abrangentes de estabilidade, aplicáveis a um espectro de regimes de fluxo, e uma exploração da dinâmica assintótica do balanço de energia durante movimentos de fluidos. A principal contribuição deste estudo encontra-se na sua abordagem metódica à aproximação numérica de equações não estacionárias de Navier-Stokes dentro de regimes turbulentos utilizando o Modelo Smagorinsky (SM). A adoção de uma discretização temporal semi-implícita com o método de Euler, aliada a uma análise meticulosa do balanço de energia, estabelece uma base robusta e adaptável a diversas condições de fluxo.Universidade Federal de Viçosa - UFV2024-01-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufv.br/jcec/article/view/1757910.18540/jcecvl10iss01pp17579The Journal of Engineering and Exact Sciences; Vol. 10 No. 1 (2024); 17579The Journal of Engineering and Exact Sciences; Vol. 10 Núm. 1 (2024); 17579The Journal of Engineering and Exact Sciences; v. 10 n. 1 (2024); 175792527-1075reponame:The Journal of Engineering and Exact Sciencesinstname:Universidade Federal de Viçosa (UFV)instacron:UFVenghttps://periodicos.ufv.br/jcec/article/view/17579/9142Copyright (c) 2024 The Journal of Engineering and Exact Scienceshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessSantos, Rômulo Damasclin Chaves dosSales, Jorge Henrique de OliveiraSilva, Alice Rosa da2024-03-26T17:19:32Zoai:ojs.periodicos.ufv.br:article/17579Revistahttp://www.seer.ufv.br/seer/rbeq2/index.php/req2/oai2527-10752527-1075opendoar:2024-03-26T17:19:32The Journal of Engineering and Exact Sciences - Universidade Federal de Viçosa (UFV)false |
dc.title.none.fl_str_mv |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes Uno Un análisis matemático para la solución débil aproximada del modelo de Smagorinsky para diferentes regímenes de flujo Un Une analyse mathématique pour la solution faible approchée du modèle de Smagorinsky pour différents régimes d'écoulement Uma análise matemática para a solução fraca aproximada do Modelo Smagorinsky para diferentes regimes de fluxo |
title |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
spellingShingle |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes Santos, Rômulo Damasclin Chaves dos Smagorinsky model. Weak Solution. Navier–Stokes equations. Asymptotic Balance. Modelo de Smagorinsky. Solução Fraca. Equações de Navier–Stokes. Balanço Assintótico. Modelo de Smagorinsky. Solución débil. Ecuaciones de Navier-Stokes. Modèle Smagorinsky. Solution faible. Équations de Navier-Stokes. |
title_short |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
title_full |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
title_fullStr |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
title_full_unstemmed |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
title_sort |
A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes |
author |
Santos, Rômulo Damasclin Chaves dos |
author_facet |
Santos, Rômulo Damasclin Chaves dos Sales, Jorge Henrique de Oliveira Silva, Alice Rosa da |
author_role |
author |
author2 |
Sales, Jorge Henrique de Oliveira Silva, Alice Rosa da |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Santos, Rômulo Damasclin Chaves dos Sales, Jorge Henrique de Oliveira Silva, Alice Rosa da |
dc.subject.por.fl_str_mv |
Smagorinsky model. Weak Solution. Navier–Stokes equations. Asymptotic Balance. Modelo de Smagorinsky. Solução Fraca. Equações de Navier–Stokes. Balanço Assintótico. Modelo de Smagorinsky. Solución débil. Ecuaciones de Navier-Stokes. Modèle Smagorinsky. Solution faible. Équations de Navier-Stokes. |
topic |
Smagorinsky model. Weak Solution. Navier–Stokes equations. Asymptotic Balance. Modelo de Smagorinsky. Solução Fraca. Equações de Navier–Stokes. Balanço Assintótico. Modelo de Smagorinsky. Solución débil. Ecuaciones de Navier-Stokes. Modèle Smagorinsky. Solution faible. Équations de Navier-Stokes. |
description |
This study delves into the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes, employing the Smagorinsky Model (SM). By treating the model as inherently discrete, we implement a semi-implicit time discretization using the Euler method. This approach includes comprehensive stability analyses, applicable to a spectrum of flow regimes, and an exploration of the asymptotic energy balance dynamics during fluid movements. The primary contribution of this study is found in its methodical approach to the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes using the Smagorinsky Model (SM). The adoption of a semi-implicit time discretization with the Euler method, coupled with a meticulous analysis of energy balance, establishes a robust foundation adaptable to diverse flow conditions. |
publishDate |
2024 |
dc.date.none.fl_str_mv |
2024-01-03 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ufv.br/jcec/article/view/17579 10.18540/jcecvl10iss01pp17579 |
url |
https://periodicos.ufv.br/jcec/article/view/17579 |
identifier_str_mv |
10.18540/jcecvl10iss01pp17579 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.ufv.br/jcec/article/view/17579/9142 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2024 The Journal of Engineering and Exact Sciences https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2024 The Journal of Engineering and Exact Sciences https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Viçosa - UFV |
publisher.none.fl_str_mv |
Universidade Federal de Viçosa - UFV |
dc.source.none.fl_str_mv |
The Journal of Engineering and Exact Sciences; Vol. 10 No. 1 (2024); 17579 The Journal of Engineering and Exact Sciences; Vol. 10 Núm. 1 (2024); 17579 The Journal of Engineering and Exact Sciences; v. 10 n. 1 (2024); 17579 2527-1075 reponame:The Journal of Engineering and Exact Sciences instname:Universidade Federal de Viçosa (UFV) instacron:UFV |
instname_str |
Universidade Federal de Viçosa (UFV) |
instacron_str |
UFV |
institution |
UFV |
reponame_str |
The Journal of Engineering and Exact Sciences |
collection |
The Journal of Engineering and Exact Sciences |
repository.name.fl_str_mv |
The Journal of Engineering and Exact Sciences - Universidade Federal de Viçosa (UFV) |
repository.mail.fl_str_mv |
|
_version_ |
1808845241458884608 |