The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Study on Numerical and Modelling Errors in LES Using a Priori and a Posteriori Testing

Tellervo Brandt

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Mechanical Engineering for public examination and debate in Auditorium K216 at Helsinki University of Technology (Espoo, Finland) on the 2nd of March, 2007, at 12 noon.

Dissertation in PDF format (ISBN 978-951-22-8635-5)   [1527 KB]
Dissertation is also available in print (ISBN 978-951-22-8634-8)

Abstract

Large eddy simulation (LES) is an approach to numerical simulation of turbulent flows. The so-called large scales are solved from the Navier–Stokes equations and the effect of the subgrid scales (SGS) is modelled. This thesis concentrates on the numerical and modelling error of LES where second-order finite-difference schemes and simple SGS models are applied. The work is restricted to these methods because they are often applied in practical LES, and some groups have reported results concerning a large numerical error related to low-order finite-difference-type schemes when compared to the effect of the SGS model. The research work of this thesis is divided into three parts. First, the error components are studied a priori. The focus is on a priori testing of the explicit filtering of the non-linear convection term of the Navier–Stokes equations, which has been suggested as a method to reduce the numerical error. In the second part, explicit filtering is applied in actual LES. The aim is to clarify if it is possible to improve the actual simulation results by explicit filtering as suggested by the a priori studies. In addition, the use of implicit filtering provided by both eddy-viscosity-type models and so-called subfilter-scale (SFS) models are compared to explicit filtering. In the third part, the error components are studied a posteriori using so-called grid-independent LES with and without explicit filtering and the Richardson extrapolation. The aims are related to separating the error components, clarifying the effect of explicit filtering, grid resolution and SGS model parameters on the components and to comparing the approaches. As a test case, a fully developed turbulent channel flow between two parallel walls is applied in all three parts of the thesis. The results of the a priori tests suggest that explicit filtering of the non-linear convection term effectively reduces the numerical error and increases the effect of the SGS model. However, in the actual performed simulations, explicit filtering increased the total simulation error and decreased the effect of the applied SGS models. Based on the performed a posteriori tests, in actual simulations with the standard Smagorinsky model, the numerical and modelling error are of the same magnitude, and explicit filtering with a smooth filter introduces a third error component which is larger than the other two error components. Of the applied approaches, the a posteriori tests using the grid-independent LES explain the behaviour of the actual simulations. The numerical error predicted by the a priori tests is too large and the effect of SGS modelling and explicit filtering are not properly described. The Richardson extrapolation for the numerical error is not valid at the applied grid resolution.

Keywords: CFD, LES, a posteriori testing, numerical error, modelling error, explicit filtering

This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

© 2007 Helsinki University of Technology


Last update 2011-05-26