Variational Multiscale Methods for incompressible flows. (8th January 2008)

• Record Type: Journal Article
• Authors: Gravemeier, V.; Lenz, S.; Wall, W.A.
• Is Part Of: International journal of computing science and mathematics. Volume 1:Number 2/3/4(2007)
• Page Start: 444
• Page End: 466
• Publication Date: 2008-01-08
• Subjects: incompressible flow -- turbulence -- large eddy simulation -- LES -- variational multiscale method -- VMM -- scale separation -- turbulent flows -- finite element method -- FEM -- finite volume method -- FVM; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.