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Colloquium March 15

Date: Thursday March 15

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: John Volker of Universität Saarlandes

Title: Finite Element Variational Multiscale Methods for Incompressible Turbulent Flows

Abstract

Variational Multiscale Methods (VMS) for the simulation of incompressible turbulent flows rely upon a decomposition of the flow into three scales: (resolved) large scales, resolved small scales, and unresolved scales. A key feature of these methods consists in applying a so--called turbulent viscosity directly only to the resolved small scales. The turbulent viscosity influences the behavior of the large scales indirectly by the coupling of the scales.

The realization of a VMS in the context of finite element methods offers different possibilities. For instance, finite element spaces for the large scales and the resolved small scales have to be chosen. One approach consists in using standard velocity/pressure finite elements for the large scales and local, high order finite elements (bubble functions) for the resolved small scales, e.g., see [Gravemeier, et al.]. An alternative approach uses standard velocity/pressure finite element spaces for all resolved scales and an additional large scale space for the velocity deformation tensor [John and Kaya]. Another aspect which might influence the efficiency of the numerical simulations considerably is the treatment of the terms which are introduced by the VMS within the time stepping scheme, see [John, et al.] for results for convection--diffusion equations.

We will give an overview about different possibilities of realizing a VMS within the finite element method, address analytical and implementational issues and present numerical studies.

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