| Títol: | 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 |
| Autor: | Badia Rodríguez, Santiago I.
Codina, Ramon
Gutiérrez Santacreu, Juan Vicente |
| Altres autors/autores: | Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria |
| Matèries: | Àrees temàtiques de la UPC::Enginyeria civil
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Long-term stability
Absorbing set
Global attractor
Stabilized finite element methods
Sub-grid scales
Navier-Stokes equations
Navier-Stokes problem
Equacions de Navier-Stokes
65N30
35Q30 |
| Tipus de document: | Article |
| Descripció: | 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 modeled. 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 spacein L2 sense. We analyze the long-term behavior of the algorithm, proving the existence of appropriate absorbing setsand a compact global attractor. The improvements with respect to a finite element Galerkin approximation are thelong-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. |
| Altres identificadors i accés: | http://hdl.handle.net/2117/3033 |
| Disponible al dipòsit: | E-prints UPC
|
| Comparteix: |
|
Tots els ítems dipositats a UPCommons estan protegits per drets d'autor.
|
