Studies of turbulence and its modelling through large eddy- and direct numerical simulation

by Alvelius, Krister

This thesis deals with numerical simulations of turbulence in simple ow cases. Both homogeneous turbulence and turbulent plane channel ow are computed, either through direct numerical simulations (DNS) or through large eddy simulations (LES) where the e ect of the smallest scales, the subgrid-scales (SGS), are modelled. The simple ow cases allow the use of pseudo spectral methods which yield a very accurate discretization and allow the focus to be put on the turbulence dynamics rather than the details of the numerical methods. The DNS methodology is a cornerstone in turbulence research and allows for detailed studies of turbulence dynamics and structures. DNS has been performed for the rotating channel ow, where many complicated features of turbulence have been explored. New insights into the generation of large elongated structures in this ow were gained through these computations. DNS was also used for statistical stationary homogeneous turbulence, where a forcing method was developed which extends the range of useful DNS. The DNS results from the rotating channel ow havealso been used in the development of SGS models for LES. In the homogeneous turbulence case LES is used with simple SGS models to investigate the features of high Reynolds number turbulence dynamics, and to determine weather accurate high Reynolds number calibrations of standard statistical turbulence models can be obtained. The stochastic approach is adopted to describe the random behaviour of the subgrid-scales in the plane channel ow. This strongly increases the variance and reduces the length scale of the model, while the mean behaviour is unchanged. A large e ort has been put in the optimization of the numerical codes on various super computers to increase the e ective Reynolds number in the simulations. Descriptors: Turbulence, Direct numerical simulation, Large eddy simulation, Homogeneous ow, Plane channel ow, subgrid-scales, parallel computers Preface This thesis considers Large eddy simulation and direct numerical simulation of simple ows. The thesis is based on the following papers. Paper 1. Alvelius, K. and Johansson, A. V. and Hallback, M. 1999 `An LES study of the Smagorinsky model and calibration of slow-pressure strain rate models' submitted toEuropean Journal of Mechanics/B Fluids Paper 2. Alvelius, K. 1999 `Random Forcing of three-dimensional homogeneous turbulence' in Physics of Fluids A, 11 (7), 1880{1889 Paper 3. Alvelius, K. and Johansson, A. V. 1999 `LES computations and comparison with Kolmogorov theory for two-point pressure-velocity correlations and structure functions for globally anisotropic turbulence' accepted for publication in Journal of Fluid Mechanics Paper 4. Alvelius, K. 1999 `A pseudo spectral method for LES of homogeneous turbulence' Paper 5. Alvelius, K. and Johansson, A. V. 1999 `Stochastic Modelling in LES of a turbulent channel ow with and without system rotation' Paper 6. Alvelius, K. and Johansson, A. V. 1999 `DNS of rotating turbulent channel ow atvarious Reynolds numbers and Rotation numbers' submitted to Journal of Fluid Mechanics Paper 7. Alvelius, K. and Skote, M. 1999 `The performance of a spectral simulation code for turbulence on parallel computers with distributed memory' submitted to SIAM Journal on Statistical and Scienti c Computing The papers are here re-set in the present thesis format. Some of them are based on publications in conference proceedings [3], [2] , [4], [7] .