This monthly seminar is intended for the PhD Students of BIMoS (members and fellows) to informally discuss topics in the field of mathematical modeling, simulation, and optimization. The aim is to develop a useful network and to help each other in this very interdisciplinary field. Occasionally, other members of the BIMoS faculty will also be invited to discuss selected problems.

DateTalk byTitleAbstract
28.06.2019Sophie KnechtelAdjoint solutions of the averaged Navier-Stokes equations for the 2D turbulent free shear flow (paper presentation)The adjoint optimization approach gained great popularity in recent years due to its ability to optimize a scalar quantity with respect to an arbitrary number of parameters, without increasing computational costs. Unfortunately it fails when used to optimize long-time averaged quantities of turbulent flows. Here the linearity of the approach does not agree with the chaotic nature of turbulence. In this paper we present a toy problem, the two dimensional turbulent free shear flow, for which we show a way to use the linear model nonetheless, i.e. by directly linearizing the time-averaged Navier-Stokes equations. This bears other problems, namely the necessity to model the non-linear time-averaged terms of the Navier-Stokes equation (such as the "Reynolds-stresses"). We can show that this modeling can be omitted for the 2D turbuelnt free shear flow and that an adjoint optimization is therefore possible. Connections to mean flow analysis are discussed and the hypothesis is introduced that the conditions for the validity of mean flow analysis are the same than the ones garanteeing the possibility of adjoint optimization in the here presented manner.