Variational Multiscale Methods for incompressible flows
by V. Gravemeier, S. Lenz, W.A. Wall
International Journal of Computing Science and Mathematics (IJCSM), Vol. 1, No. 2/3/4, 2007

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.

Online publication date: Mon, 07-Jan-2008

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