Variational Multiscale Methods for incompressible flows

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

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11 Scopus citations


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.

Original languageEnglish
Pages (from-to)444-466
Number of pages23
JournalInternational Journal of Computing Science and Mathematics
Issue number2-4
StatePublished - 2007


  • LES
  • VMM
  • incompressible flow
  • large eddy simulation
  • scale separation
  • turbulence
  • variational multiscale method


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