Three regularization models of the Navier-Stokes equations

Mostrar todas las versiones(3)

We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A.
Formato:	Artículo publishedVersion
Lenguaje:	Inglés
Publicado:	2008
Materias:	Approximation theory Direct numerical simulation Mathematical models Navier Stokes equations Reynolds number Energy spectrum Subfilter-scale physics Subgrid-scale (SGS) models Flow of fluids
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_10706631_v20_n3_p_Graham
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paperaa:paper_10706631_v20_n3_p_Graham
record_format	dspace
spelling	paperaa:paper_10706631_v20_n3_p_Graham2023-06-12T16:49:23Z Three regularization models of the Navier-Stokes equations Phys. Fluids 2008;20(3) Graham, J.P. Holm, D.D. Mininni, P.D. Pouquet, A. Approximation theory Direct numerical simulation Mathematical models Navier Stokes equations Reynolds number Energy spectrum Subfilter-scale physics Subgrid-scale (SGS) models Flow of fluids Approximation theory Direct numerical simulation Flow of fluids Mathematical models Navier Stokes equations Reynolds number We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier-Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re≈3300, Taylor Reynolds number of Re≈790, and to a direct numerical simulation (DNS) of the Navier-Stokes equations. We derive the de Kármán-Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k-1 energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼k1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán-Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α. © 2008 American Institute of Physics. Fil:Mininni, P.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10706631_v20_n3_p_Graham
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language	Inglés
orig_language_str_mv	eng
topic	Approximation theory Direct numerical simulation Mathematical models Navier Stokes equations Reynolds number Energy spectrum Subfilter-scale physics Subgrid-scale (SGS) models Flow of fluids Approximation theory Direct numerical simulation Flow of fluids Mathematical models Navier Stokes equations Reynolds number
spellingShingle	Approximation theory Direct numerical simulation Mathematical models Navier Stokes equations Reynolds number Energy spectrum Subfilter-scale physics Subgrid-scale (SGS) models Flow of fluids Approximation theory Direct numerical simulation Flow of fluids Mathematical models Navier Stokes equations Reynolds number Graham, J.P. Holm, D.D. Mininni, P.D. Pouquet, A. Three regularization models of the Navier-Stokes equations
topic_facet	Approximation theory Direct numerical simulation Mathematical models Navier Stokes equations Reynolds number Energy spectrum Subfilter-scale physics Subgrid-scale (SGS) models Flow of fluids Approximation theory Direct numerical simulation Flow of fluids Mathematical models Navier Stokes equations Reynolds number
description	We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier-Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re≈3300, Taylor Reynolds number of Re≈790, and to a direct numerical simulation (DNS) of the Navier-Stokes equations. We derive the de Kármán-Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k-1 energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼k1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán-Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α. © 2008 American Institute of Physics.
format	Artículo Artículo publishedVersion
author	Graham, J.P. Holm, D.D. Mininni, P.D. Pouquet, A.
author_facet	Graham, J.P. Holm, D.D. Mininni, P.D. Pouquet, A.
author_sort	Graham, J.P.
title	Three regularization models of the Navier-Stokes equations
title_short	Three regularization models of the Navier-Stokes equations
title_full	Three regularization models of the Navier-Stokes equations
title_fullStr	Three regularization models of the Navier-Stokes equations
title_full_unstemmed	Three regularization models of the Navier-Stokes equations
title_sort	three regularization models of the navier-stokes equations
publishDate	2008
url	http://hdl.handle.net/20.500.12110/paper_10706631_v20_n3_p_Graham
work_keys_str_mv	AT grahamjp threeregularizationmodelsofthenavierstokesequations AT holmdd threeregularizationmodelsofthenavierstokesequations AT mininnipd threeregularizationmodelsofthenavierstokesequations AT pouqueta threeregularizationmodelsofthenavierstokesequations
_version_	1769810344157380608

Three regularization models of the Navier-Stokes equations

Ejemplares similares