@MASTERSTHESIS\{IMM2013-06665,
    author       = "R. E. Christiansen",
    title        = "Advanced Techniques for Investigating Structures in Computational Fluid Dynamics",
    year         = "2013",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Matematiktorvet, Building 303B, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisors: Professor Morten Br{\o}ns, and Associate Professor Allan P. Engsig-Karup, apek@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "The problems of incompressible fluid flow past a cylinder in free flow and past a cylinder near a moving wall in two dimensions are studied numerically. Here the velocity and pressure fields are obtained using a spectral element method based solver. The study is performed for Reynolds numbers in the low end of the periodic shedding regime and is mainly concerned with analysing vortex structures existing behind the cylinder, with main focus on the vortices surviving downstream. A vortex is defined uniquely as an extremum in vorticity and this definition is used to implement an algorithm for identifying and tracing vortices. A way of assuring that periodicity in the numerical solution has been reached using the tracing method is presented.
The Reynolds number, time and ratio of cylinder diameter to distance from the wall are identified as the only independent parameters of the problems. Dynamical systems theory is used to analyse changes in the vortex structures as the independent parameters are varied. Here, two types of bifurcations are identified and characterised using existing theory. Also, all different structures for vorticity extrema and saddle-points observed in the considered parameter range are identified and described.
The stabilizing effect of the wall is mapped. The effects of the wall and Reynolds number on the shedding frequency, creation point and pathway followed by the vortices are investigated. The decrease in magnitude of a vortex as it travels through the fluid is investigated and a nearly constant decrease rate is found far downstream.
A small scale investigation of collocation based uncertainty quantification is performed where the Reynolds number is taken to be the input parameter containing uncertainty. First, the cylinder in free flow is treated and the Strouhal number and pressure induced drag are considered as functions of the uncertain Reynolds number. Secondly, the cylinder near the moving wall is treated and the path followed by a vortex downstream and its magnitude as a function of the Reynolds number investigated.
Used theoretical concepts from dynamical systems theory, polynomial approximation theory, the spectral element method and uncertainty quantification are included. So are explanations of the software used and developed for the simulations and post processing readying the data for the final analysis.
Most of the methods used in this work have not been adapted by the industry (yet)."
}