ISBN 978-3-8439-1670-7

978-3-8439-1670-7, Reihe Mathematik

Matthias Frankenbach
An Adjoint Based A Posteriori Error Estimator for Moving Meshes in Large Eddy Simulations

143 Seiten, Dissertation Technische Universität Darmstadt (2014), Softcover, A5

Zusammenfassung / Abstract

As the computational effort increases dramatically with finer resolutions of the computational domain, the discipline of mesh design has become a separate part of Computational Fluid Dynamics (CFD). Not only the resolution of the underlying meshes but also utilized models for turbulent problems are a point of action to tackle simulation accuracy.

Large Eddy Simulations (LES) are an accepted and favored technique to simulate turbulent flows and an improvement of the simulation quality with a fixed number of degrees of freedom is desired and investigated in this work. As the concept of LES is to resolve large scales, where large is a grid dependent concept, a refinement in flow active regions of a turbulent flow usually leads to more accurate results but in general these regions are not known. The concepts of mesh refinement are concerned with localizing these flow active regions and changing the mesh there for more accurate simulations.

This work, is concerned with an automated mesh design approach for LES of turbulent flows based on a dynamic moving mesh partial differential equation (MMPDE) redistributing gridpoints and thereby keeping the computational effort of a CFD simulation nearly fixed. Adjoint based information is used to determine regions of the flow field that are most sensitive to certain target quantities and, derived by a dual weighted residual method (DWRM), more general quantities of interest (QoI) are investigated and compared to physical motivated ones. In this context an adjoint based a posteriori error estimator is derived, which assesses the quality of numerical and subgrid modeling contributions of an LES.

The quality of this new method is compared to a highly resolved LES reference solution as well as the best so far known physical-based approaches for a flow over periodic hills. The contribution of the subscale model is given special attention in this context. The great potential of moving mesh methods to efficiently improve the resolution of turbulent flow features is shown, while the underlying approach is further improved, providing a tool to modify and enhance numerical grids for LES.