Colloquium Mathematics - Prof. Dr. Volker John Weierstrass Institute for Applied Analysis and Stochastics & Freie Universität Berlin

Title: Variational Multiscale (VMS) Methods for the Simulation of Turbulent Incompressible Flows

Abstract:

VMS methods are a comparably new class of methods for simulating convection-dominated problems, like turbulent incompressible flows. The talk will start with an introduction  to the difficulties of turbulent flow simulations. Next, principal ideas of the  classical Large Eddy Simulation (LES) approach will be presented. Then, the basic  ideas of VMS methods will be discussed, together with highlighting the differences to  LES methods.  Various realizations of VMS methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this talk, the derivation of the different VMS methods is presented in some detail,  their relation among each other and  their behavior in numerical simulations are discussed.