Title: Variational Multiscale Methods for incompressible flows

Authors: V. Gravemeier, S. Lenz, W.A. Wall

Addresses: Technical University of Munich, Germany. ' The Linde Group, Munich, Germany. ' Technical University of Munich, Germany

Abstract: The present paper reviews the Variational Multiscale Method (VMM) as a framework enabling the development of computational methods for the simulation of incompressible flows, particularly in the form of Large Eddy Simulations (LESs) of turbulent flows. Starting with a variational formulation of the Navier–Stokes equations, a separation of all scales of the flow problem into two and three scale groups, respectively, is shown. A particular numerical method emanating from both the two- and the three-scale separation, respectively, is described, one of them in the form of a Finite Element Method (FEM) and the other one in the form of a Finite Volume Method (FVM). Respective numerical examples illustrate the suitability of both variants of the VMM for the numerical simulation of turbulent flows.

Keywords: incompressible flow; turbulence; large eddy simulation; LES; variational multiscale method; VMM; scale separation; turbulent flows; finite element method; FEM; finite volume method; FVM.

DOI: 10.1504/IJCSM.2007.016545

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.444 - 466

Published online: 07 Jan 2008 *

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