Título:
|
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/a:
|
Badia, Santiago; Codina, Ramon; Gutiérrez Santacreu, Juan Vicente
|
Otros autores:
|
Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus; Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria |
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 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. |
Materia(s):
|
-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 |
Derechos:
|
|
Tipo de documento:
|
Artículo |
Compartir:
|
|