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Long term stability estimates and existence of a global attractor in a finite element approximation of the Navier-Stokes equations with numerical sub-grid scale modeling
dc.contributor.author | Badia, Santiago |
dc.contributor.author | Codina, Ramon |
dc.contributor.author | Gutiérrez Santacreu, Juan Vicente |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria |
dc.date.accessioned | 2012-04-18T18:07:25Z |
dc.date.available | 2012-04-18T18:07:25Z |
dc.date.created | 2012 |
dc.date.issued | 2012 |
dc.identifier.citation | S. Badia; Codina, R.; Gutiérrez, J. V. Long term stability estimates and existence of a global attractor in a finite element approximation of the Navier-Stokes equations with numerical sub-grid scale modeling. A: Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada. "XXI Congreso de Ecuaciones Diferenciales y Aplicaciones, XI Congreso de Matem´atica Aplicada". Ciudad Real: 2012, p. 1-8. |
dc.identifier.uri | http://hdl.handle.net/2117/15744 |
dc.description.abstract | Variational multiscale methods lead to stable finite element approximations of the Navier-Stokes equations, both dealing with the indefinite nature of the system (pressure stability) and the velocity stability loss for high Reynolds numbers. These methods enrich the Galerkin formulation with a sub-grid component that is modelled. In fact, the effect of the sub-grid scale on the captured scales has been proved to dissipate the proper amount of energy needed to approximate the correct energy spectrum. Thus, they also act as effective large-eddy simulation turbulence models and allow to compute flows without the need to capture all the scales in the system. In this article, we consider a dynamic sub-grid model that enforces the sub-grid component to be orthogonal to the finite element space in L2 sense.We analyze the long-term behavior of the algorithm, proving the existence of appropriate absorbing sets and a compact global attractor. The improvements with respect to a finite element Galerkin approximation are the long-term estimates for the sub-grid component, that are translated to effective pressure and velocity stability. Thus, the stabilization introduced by the sub-grid model into the finite element problem is not deteriorated for infinite time intervals of computation. |
dc.format.extent | 8 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
dc.subject.lcsh | Navier-Stokes equations--Numerical solutions |
dc.subject.other | dynamic sub-grid scales |
dc.subject.other | Navier-Stokes problem |
dc.subject.other | long-term stability |
dc.subject.other | absorbing set |
dc.subject.other | global attractor |
dc.subject.other | stabilized finite element methods |
dc.subject.other | orthogonal sub-grid scales |
dc.title | Long term stability estimates and existence of a global attractor in a finite element approximation of the Navier-Stokes equations with numerical sub-grid scale modeling |
dc.type | Conference report |
dc.subject.lemac | Equacions de Navier-Stokes |
dc.contributor.group | Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus |
dc.relation.publisherversion | http://matematicas.uclm.es/cedya09/archive/textos/58_Badia-S.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 10254750 |
dc.description.version | Postprint (published version) |
local.citation.author | S. Badia; Codina, R.; Gutiérrez, J. V. |
local.citation.contributor | Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada |
local.citation.pubplace | Ciudad Real |
local.citation.publicationName | XXI Congreso de Ecuaciones Diferenciales y Aplicaciones, XI Congreso de Matem´atica Aplicada |
local.citation.startingPage | 1 |
local.citation.endingPage | 8 |