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Numerical Methods in Turbulence

Manica, Carolina Cardoso (2006) Numerical Methods in Turbulence. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Fluid motion and its richness of detail are described by theNavier-Stokes equations. Most of the numerical analysis existent todate is applicable for strong solutions (typically small body forceand initial data). We prove that statistics of weak solutions areoptimally computable in the simple but important case of small bodyforce and large initial data. These estimates are used to predictdrag and lift statistics, quantities of great interest inengineering. In the case of arbitrarily large body force and initialdata, for shear flows, statistics of the computed solution are shownto behave according to the Kolmogorov theory.Many times, in turbulent fluid flow, a direct numerical simulationbecomes expensive. One alternative is Large Eddy Simulation (LES).It exploits the decoupling of scales, achieved via introduction of afilter, thus reducing the number of degrees of freedom in asimulation. A relatively new family of LES models is the ApproximateDeconvolution Models (ADM). They have remarkable mathematicalproperties and perform well in computations. However, some reportsclaim that they are unstable for simulations with walls and requirethe addition of explicit stabilization.We show that, given the right formulation, variationaldiscretizations of the Zeroth Order Model, a member of the ADMfamily, are indeed stable. We present evidence that stability of oneformulation is sensitive to the exact way in which filtering isperformed and show some numerical results. An alternativeformulation, which does not depend on the way filtering isperformed, is also presented. In both cases we perform convergencestudies. This is a first step in determining stable and robustdiscretizations for the whole family of ADM, as well as guidance fordealing with arbitrary geometries/domains that arise in practicalapplications.Getting a prediction of a turbulent flow right also means gettingthe energy balance and the rotational structures correct, whichmeans (in the large) matching the energy and helicity statistics. Weapply similarity theory to the ADM and show that the model has ahelicity cascade, linked to its energy cascade, which predicts thecorrect helicity statistics up to the cut-off frequency.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Manica, Carolina Cardosocac15@pitt.eduCAC15
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.eduWJL
Committee MemberRiviere,
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberErvin,
Date: 29 September 2006
Date Type: Completion
Defense Date: 7 July 2006
Approval Date: 29 September 2006
Submission Date: 3 August 2006
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Approximate Deconvolution Models; Differential Filter; Large Eddy Simulation; Navier-Stokes equations; Time Averages; Turbulence
Other ID:, etd-08032006-104013
Date Deposited: 10 Nov 2011 19:56
Last Modified: 15 Nov 2016 13:47


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