Si avvisa che Mercoledi' 3 dicembre alle ore 15 30, presso la sala seminari del Dipartimento di Matematica Applicata (V. Bonanno)
il Prof. Volker John (Otto-von-Guericke-Universitaet, Magdeburg)
terra' un seminario
Titolo: Analytical and numerical aspects in the simulation of turbulent flows with Large Eddy Simulation and Variational MultiScale methods
Abstract: The space averaged Navier-Stokes equations are the basic equations of LES. In the first part of the talk, analytical studies of a so-called commutation error will be presented. This error occurs in the derivation of the space averaged Navier-Stokes equations in a bounded domain. We will present models for the Reynolds stress tensor which are based on an approximation of the Fourier transform of the filter function. Next, the discretization of the LES models with second order implicit discretizations in time and with finite element discretizations in space is described. The solution of the discrete problems requires the solution of large linear saddle point equations. We will describe a multilevel approach which uses stable non-conforming finite element discretizations on the coarser levels of the grid hierarchy. A numerical study of the considered LES models will be presented.
The problems of classical LES in a bounded domain motivate a different definition of the large scales, namely be projection into subspaces as in the variational multiscale method (VMS). The second part of the talk presents a new type of VMS where the fluctuations (small scales) can cross mesh cell boundaries. A finite element error analysis of this method is given, its implementation is discussed and a numerical study will be presented
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