Variational multiscale methods for incompressible flows

The present article reviews the variational multiscale method as a framework enabling the development of computatinal methods for the simulation of incompressible flows, particularly in the form of large eddy simulations 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 three-scale separation, respectively, is described, one of them in the form of a finite element method and the other one in the form of a finite volume method. Respective numerical examples illustrate the suitability of both variants of the variational multiscale method for the numerical simulation of turbulent flows.     «

The present article reviews the variational multiscale method as a framework enabling the development of computatinal methods for the simulation of incompressible flows, particularly in the form of large eddy simulations 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 three-scale separati...     »